Adaptive power matching method and device for receiving system

Abstract

The present invention discloses an adaptive power matching method and device for a receiving system, the method comprising collecting power signals, constructing geodesic equations for decomposition, generating geometric eigenvectors, and calculating stability indicators; constructing standardized characteristic matrices, obtaining expansion coefficient sequences, and calculating fusion entropy features and information completeness indicators; performing recursive decomposition, obtaining spectrum eigenvectors and modal parameter sets; constructing a hybrid prediction model, obtaining prediction confidence and prediction value sequences; performing multi-objective constraint optimization, obtaining an optimized solution and constraint satisfaction; performing feedback correction and stability analysis, and outputting a correction control amount; performing self-optimization feedback regulation, and outputting an optimized parameter set; calculating a power adjustment control signal and executing power adjustment, and obtaining an adjusted actual power value; performing closed-loop correction, and realizing adaptive power matching control. The present invention realizes automatic, efficient, and accurate power matching, and improves the stability and reliability of the system.

Description

Technical Field

[0001] The present invention belongs to the field of electronic countermeasures, and particularly relates to an adaptive power matching method and device for a receiving system. Background Art

[0002] In modern electronic countermeasure systems, power matching control of the receiving system is a key technology to ensure system performance. With the increasingly complex electronic countermeasure environment and the continuous upgrading of the opponent's interference means, the receiving system faces a wider power dynamic range, a faster power change speed, and more diverse interference forms. Precise power matching control directly affects the dynamic range, signal detection probability, and anti-interference ability of the receiving system, and is of great significance for improving the overall system performance. Especially in a high-intensity electronic countermeasure environment, the receiving system needs to complete power adaptive adjustment within microseconds, which poses extremely high requirements on power matching control technology.

[0003] Currently, common power matching control methods mainly include closed-loop control based on PID, look-up table method, and neural network and other schemes. The PID-based method realizes power control by adjusting the proportional, integral, and differential parameters, but its linear control characteristics are difficult to cope with strongly nonlinear power changes. The look-up table method controls through the pre-calibrated power-attenuation correspondence relationship, but the number of table items is limited, and the interpolation error is large in rapidly changing scenarios. Although the neural network-based method has the ability of nonlinear mapping, network training depends on a large amount of sample data, and the real-time processing speed is difficult to meet the microsecond-level response requirements. At the same time, existing methods generally adopt a fixed-window data processing mechanism, which is prone to overshoot and oscillation when the signal changes suddenly.

[0004] The existing technical solutions have the following specific problems: First, the non-stationary characteristics of power signals are difficult to accurately characterize. Especially in scenarios such as Doppler frequency shift and phase jump, traditional Fourier analysis methods are difficult to depict the instantaneous characteristics of signals; the dimensionality reduction projection in the feature extraction process will lose the geometric structure information of the signal, resulting in a decrease in control accuracy; the prediction model does not consider the probability evolution characteristics of the system state, and the reliability of the prediction results is insufficient; the robustness constraint in the controller design is too conservative, affecting the dynamic response performance of the system; the compensation strategy lacks multi-scale analysis of errors and is difficult to achieve precise closed-loop correction. In addition, the communication delay and sampling error of the digital control interface will also affect the control accuracy. These technical problems seriously restrict the power matching performance of the receiving system in a complex electronic countermeasure environment. Summary of the Invention

[0005] The object of the invention is to provide an adaptive power matching method and device for a receiving system to solve the above problems existing in the prior art.

[0006] Technical Solution: An adaptive power matching method for a receiving system includes the following steps:

[0007] S1. Collect the power signal of the acquisition and reception system and convert it into a power sequence; project the power sequence onto the Riemannian manifold, construct a geodesic equation for decomposition to obtain an intrinsic mode function set; calculate the Riemannian metric tensor based on the intrinsic mode function set to generate a geometric feature vector; perform dynamic singular value decomposition on the power sequence based on the geometric feature vector to obtain a dynamic feature matrix and a principal singular value sequence; calculate the topological entropy based on the dynamic feature matrix and the principal singular value sequence; calculate the stability index based on the topological entropy and the principal singular value sequence.

[0008] S2. Calculate the dynamic mean and dynamic standard deviation based on the stability index, the dynamic feature matrix, and the geometric feature vector and perform normalization processing to obtain a normalized feature matrix; perform a generalized Gegenbauer polynomial expansion on the normalized feature matrix to obtain an expansion coefficient sequence; use the variational mode decomposition method to process the normalized feature matrix to obtain a mode set; construct and solve a generalized Lasso problem based on the mode set and the expansion coefficient sequence to obtain a sparse feature representation and a feature importance index; calculate the fusion entropy feature and the information completeness index based on the sparse feature representation and the feature importance index.

[0009] S3. Perform processing using the generalized Christoffel function based on the fusion entropy feature and the information completeness index to obtain an optimal kernel function; construct a multi-level Hankel matrix based on the optimal kernel function and perform recursive decomposition to obtain a feature sequence and a dynamic feature matrix; construct and solve a probability flow equation based on the feature sequence and the dynamic feature matrix to obtain a probability distribution and a state transition matrix; construct a generalized Prony model based on the probability distribution and perform parameter estimation to obtain a spectral feature vector and a set of modal parameters; construct a hybrid prediction model based on the spectral feature vector, the set of modal parameters, and the state transition matrix to obtain a prediction confidence level and a prediction value sequence.

[0010] S4. Use the Hamilton-Jacobi framework based on the hybrid prediction model, the prediction confidence level, and the prediction value sequence to construct and solve a performance index optimization problem, and output an optimal control strategy and a performance evaluation index; construct a generalized Chebyshev controller based on the optimal control strategy and the performance evaluation index to obtain a set of controller parameters and a robustness index; construct a multi-level compensation strategy based on the set of controller parameters and the robustness index to generate a compensation signal and a compensation effect evaluation; perform multi-objective constraint optimization based on the compensation signal and the compensation effect evaluation to obtain an optimal solution and a constraint satisfaction degree; perform feedback correction and stability analysis based on the optimal solution and the constraint satisfaction degree, and output a corrected control quantity.

[0011] S5. Based on the corrected control quantity, the optimal control strategy, and the compensation signal, use the dynamic weight fusion method to generate the final control quantity and the fusion weight set; based on the final control quantity and the fusion weight set, construct a Bernstein prediction compensator to output the prediction compensation quantity; based on the final control quantity and the prediction compensation quantity, perform adaptive filtering and smoothing processing to obtain the smoothed control quantity; based on the smoothed control quantity and the pre-stored system response data, conduct real-time performance evaluation to obtain the performance evaluation result; based on the performance evaluation result and the pre-stored system operating state, conduct self-optimizing feedback regulation to output the optimization parameter set;

[0012] S6. Based on the optimization parameter set, the smoothed control quantity, and the prediction compensation quantity, calculate the power adjustment control signal and execute power adjustment to obtain the adjusted actual power value; based on the adjusted actual power value, conduct closed-loop correction to achieve adaptive power matching control and output the power matching evaluation value.

[0013] An adaptive power matching device for receiving a system, comprising:

[0014] At least one processor; and,

[0015] A memory communicatively connected to at least one of the processors; wherein,

[0016] The memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the above-mentioned adaptive power matching method for the receiving system.

[0017] Advantageous effects: The present invention realizes automatic, efficient, and precise power matching, can perform rapid real-time adjustment according to the actual environmental conditions, improves the stability and reliability of the system, and reduces manual intervention and operation time; at the same time, it also realizes precise closed-loop correction. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flowchart of the present invention.

[0019] Figure 2 is a flowchart of step S1 of the present invention.

[0020] Figure 3 is a flowchart of step S2 of the present invention.

[0021] Figure 4 is a flowchart of step S3 of the present invention.

[0022] Figure 5 is a flowchart of step S4 of the present invention.

[0023] Figure 6 is a flowchart of step S5 of the present invention.

[0024] Figure 7 This is the flowchart of step S6 of the present invention.

[0025] Figure 8 This is the structural schematic diagram of an embodiment of the present invention.

[0026] Figure 9 This is the flowchart of an embodiment of the present invention. Detailed implementation manners

[0027] As Figure 1 shown, the present application proposes an adaptive power matching method for a receiving system, including the following steps:

[0028] S1. Collect the power signal of the receiving system and convert it into a power sequence; project the power sequence onto a Riemannian manifold, construct a geodesic equation for decomposition to obtain an intrinsic mode function set; based on the intrinsic mode function set, calculate the Riemannian metric tensor to generate a geometric feature vector; based on the geometric feature vector, perform dynamic singular value decomposition on the power sequence to obtain a dynamic feature matrix and a main singular value sequence; based on the dynamic feature matrix and the main singular value sequence, calculate the topological entropy; based on the topological entropy and the main singular value sequence, calculate the stability index;

[0029] S2. Based on the stability index, the dynamic feature matrix, and the geometric feature vector, calculate the dynamic mean and the dynamic standard deviation and perform standardization processing to obtain a standardized feature matrix; perform a generalized Gegenbauer polynomial expansion on the standardized feature matrix to obtain an expansion coefficient sequence; use the variational mode decomposition method to process the standardized feature matrix to obtain a mode set; based on the mode set and the expansion coefficient sequence, construct a generalized Lasso problem and solve it to obtain a sparse feature representation and a feature importance index; based on the sparse feature representation and the feature importance index, calculate the fusion entropy feature and the information completeness index;

[0030] S3. Based on the fusion entropy feature and the information completeness index, use the generalized Christoffel function for processing to obtain an optimal kernel function; based on the optimal kernel function, construct a multi-level Hankel matrix and perform recursive decomposition to obtain a feature sequence and a dynamic feature matrix; based on the feature sequence and the dynamic feature matrix, construct a probability flow equation and solve it to obtain a probability distribution and a state transition matrix; based on the probability distribution, construct a generalized Prony model and perform parameter estimation to obtain a spectral feature vector and a modal parameter set; based on the spectral feature vector, the modal parameter set, and the state transition matrix, construct a hybrid prediction model to obtain a prediction confidence level and a prediction value sequence;

[0031] S4. Based on the hybrid prediction model, prediction confidence, and prediction value sequence, use the Hamilton-Jacobi framework to construct and solve the performance metric optimization problem, and output the optimal control strategy and performance evaluation metrics; based on the optimal control strategy and performance evaluation metrics, construct a generalized Chebyshev controller to obtain the controller parameter set and robustness metrics; based on the controller parameter set and robustness metrics, construct a multi-level compensation strategy to generate a compensation signal and compensation effect evaluation; based on the compensation signal and compensation effect evaluation, perform multi-objective constraint optimization to obtain the optimization solution and constraint satisfaction; based on the optimization solution and constraint satisfaction, perform feedback correction and stability analysis, and output the corrected control quantity;

[0032] S5. Based on the corrected control quantity, optimal control strategy, and compensation signal, use the dynamic weight fusion method to generate the final control quantity and fusion weight set; based on the final control quantity and fusion weight set, construct a Bernstein prediction compensator and output the prediction compensation quantity; based on the final control quantity and prediction compensation quantity, perform adaptive filtering and smoothing to obtain the smoothed control quantity; based on the smoothed control quantity and pre-stored system response data, perform real-time performance evaluation to obtain the performance evaluation result; based on the performance evaluation result and pre-stored system operating state, perform self-optimizing feedback regulation and output the optimization parameter set;

[0033] S6. Based on the optimization parameter set, smoothed control quantity, and prediction compensation quantity, calculate the power adjustment control signal and execute power adjustment to obtain the adjusted actual power value; based on the adjusted actual power value, perform closed-loop correction to achieve adaptive power matching control and output the power matching evaluation value.

[0034] As Figure 2 shown, according to one aspect of the present application, step S1 is further:

[0035] S11. Collect the power signal of the receiving system, and use an analog-to-digital converter with a predetermined sampling frequency to synchronously sample the power signal and output the power sequence;

[0036] S12. Based on the power sequence, construct the geodesic equation on the Riemannian manifold; use the projection operator to project the power sequence from the Euclidean space onto the Riemannian manifold to obtain the projected signal; based on the geodesic equation, decompose the projected signal to obtain the set of intrinsic mode functions;

[0037] S13. Based on the set of intrinsic mode functions, calculate the tangent space basis and construct the Riemannian metric tensor; based on the Riemannian metric tensor, calculate the Riemannian curvature; based on the Riemannian curvature, obtain the curve parameterization and unit normal vector, and calculate the geodesic curvature and shape operator; combine the Riemannian curvature, geodesic curvature, and shape operator to form the geometric feature vector;

[0038] S14. Based on the power sequence and the geometric feature vector, construct a dynamic embedding matrix for time delay and embedding dimension; calculate the dynamic window size based on the two-norm of the geometric feature vector and the standard deviation of the power sequence; perform singular value decomposition on the dynamic embedding matrix based on the dynamic window size to obtain a dynamic feature matrix and a sequence of dominant singular values.

[0039] S15. Based on the dynamic feature matrix and the sequence of dominant singular values, calculate the normalized singular values; calculate the topological entropy based on the normalized singular values; calculate the stability index based on the topological entropy, a preset reference entropy value, the variance of the sequence of dominant singular values, and the maximum singular value; determine the state identifier of the system based on the stability index.

[0040] In an embodiment of the present application, a power signal p(t), an ambient temperature T(t), and a load impedance Z(t) input by a receiving system are received, and an analog-to-digital converter with a sampling frequency of 2 MHz is used to synchronously sample the signals, outputting a discrete time series {p[n], T[n], Z[n]}, where n is the sampling point serial number and the value range is from 1 to N.

[0041] Taking the power sequence p[n] as the input, construct the geodesic equation ▽ γ' γ' = 0 on the Riemann manifold M, where γ' represents the tangent vector of the curve on the manifold and ▽ represents the Riemann connection; use the projection operator P to project the power sequence from the Euclidean space R N onto the Riemann manifold M; decompose the projected signal along the geodesic to obtain an ensemble of intrinsic mode functions {ci[n]} and a residue r[n].

[0042] Based on the ensemble of intrinsic mode functions {ci[n]}, calculate the tangent space bases ξi and ξj, and construct the Riemannian metric tensor gij = <ξi, ξj>; calculate the Riemannian curvature K = det(gij) / det(hij) based on the Riemannian metric tensor gij and the second fundamental form hij, where det represents the determinant; use the curve parameterization γ and the unit normal vector N to calculate the geodesic curvature κg = |γ''(γ'×N)| / |γ'| 3 , where γ'' represents the second derivative of the curve γ; calculate the shape operator S = -dN, where d represents the differential operator; combine the calculated Riemannian curvature K, geodesic curvature κg, and shape operator S to form the geometric feature vector F.

[0043] Taking the power sequence p[n] and the geometric feature vector F as the input, construct a dynamic embedding matrix X(t) = [x(t), x(t+τ),..., x(t+(M-1)τ)] for time delay τ and embedding dimension M; according to the two-norm ||F|| of the geometric feature vector F 2 and the standard deviation σ of the power sequence p[n], calculate the dynamic window size W(t)=α||F||2 +βσ(p[n]), where α and β are weight coefficients; perform singular value decomposition on the dynamic embedding matrix X(t) to obtain the dynamic feature matrix D(t) and the main singular value sequence λ(t).

[0044] Using the dynamic feature matrix D(t) and the main singular value sequence λ(t), calculate the normalized singular value pi(t); calculate the topological entropy H(t) = -Σpi(t)log(pi(t)) according to the normalized singular value; compare the topological entropy H(t) with the reference entropy value H 0 and combine the variance var(λ(t)) of the main singular value sequence λ(t) and the maximum singular value λ max , calculate the stability index S(t)=exp(-H(t) / H 0 )·(1 - var(λ(t)) / λ max ); determine the system state identifier flag according to the value of the stability index S(t).

[0045] In this embodiment, by projecting the power sequence onto the Riemannian manifold and combining the method of geodesic equation decomposition, an accurate characterization of the non-stationary power signal is achieved. Using a high sampling rate of 2MHz ensures the complete acquisition of fast-changing power signals; by utilizing the intrinsic properties of Riemannian geometry and decomposing the signal through the geodesic equation, an intrinsic mode function set reflecting the essential characteristics of the signal is obtained; based on the Riemannian metric tensor, Riemannian curvature, geodesic curvature, and shape operator are calculated to construct a feature vector containing the geometric characteristics of the signal; through the adaptive adjustment of the dynamic window size, an accurate capture of the non-stationary characteristics of the signal is realized; by combining dynamic singular value decomposition to obtain the dynamic feature matrix and the main singular value sequence, finally, the accurate identification and characterization of the power signal state are achieved through topological entropy and stability index. This embodiment improves the characterization accuracy of fast-changing power signals in the electronic countermeasure environment and lays a foundation for subsequent adaptive control.

[0046] According to one aspect of the present application, step S11 is further as follows:

[0047] S111. Receive the power signal p(t), the environmental temperature T(t), and the load impedance Z(t), and construct a three-dimensional signal space V={v(t)|v(t)=[p(t), T(t), Z(t)]}; use the k-means clustering algorithm to calculate k spatial centroids ci=[pi, Ti, Zi], i = 1, 2,..., k; construct a Voronoi diagram based on the spatial centroids to obtain the spatial partition boundary set B={bij} and the region set R={Ri}.

[0048] S112. Receive the spatial division boundary set B and the region set R, and calculate the signal density di = Ni / Vi of each Voronoi region Ri, where Ni is the number of data points in the region and Vi is the region volume; dynamically adjust the sampling rate fsi = fs0·(di / d0), where fs0 is the reference sampling rate of 2 MHz, d0 is the preset density threshold, and α is the adjustment coefficient; output the adaptive sampling rate sequence {fsi}. α , where fs0 is the reference sampling rate of 2 MHz, d0 is the preset density threshold, and α is the adjustment coefficient; output the adaptive sampling rate sequence {fsi}.

[0049] S113. Use the adaptive sampling rate sequence {fsi} to sample the signals in each Voronoi region Ri to obtain the initial discrete sequence {pi[m], Ti[m], Zi[m]}; perform preprocessing using a median filter with a window length Wi = β·(d0 / di), where β is the proportionality coefficient; output the filtered discrete sequence {p'i[m], T'i[m], Z'i[m]}.

[0050] S114. Receive the filtered sequence {p'i[m], T'i[m], Z'i[m]} output in step S113, and calculate the local statistical features of each sequence: the mean μi = E[x'i[m]], and the variance σi 2 = E[(x'i[m] - μi)²], where x represents p, T, Z; detect outliers according to the 3σ criterion: |x'i[m] - μi| > 3σi; output the outlier marking sequence {fi[m]}.

[0051] S115. Use the outlier marking sequence {fi[m]} and the filtered sequence as inputs, and replace the outliers using piecewise cubic spline interpolation: si(t) = ai(t - ti) 3 + bi(t - ti) 2 + ci(t - ti) + di, where the coefficients are determined by maintaining the continuity of the second derivative; combine the processing results of all Voronoi regions and output the final discrete time sequence {p[n], T[n], Z[n]} and the data quality index Q.

[0052] In this embodiment, by combining the k-means clustering and adaptive sampling techniques, high-quality signal acquisition and preprocessing are achieved. A three-dimensional signal space is constructed and the k-means clustering algorithm is used to calculate the spatial centroid. The spatial adaptive partitioning is realized through the Voronoi diagram, effectively capturing the spatial distribution characteristics of the signal. The sampling rate is dynamically adjusted based on the signal density in each Voronoi region, realizing the optimal allocation of sampling resources. The preprocessing is carried out through a median filter, and the window length is adaptively adjusted according to the signal density, effectively suppressing the sampling noise. The 3σ criterion is used for outlier detection, and data repair is realized through piecewise cubic spline interpolation, ensuring the quality of the sampled data. The finally output discrete time series has a high signal-to-noise ratio and integrity. This embodiment improves the signal acquisition quality in the electronic countermeasure environment, laying a solid foundation for subsequent feature extraction and control optimization.

[0053] According to one aspect of the present application, step S14 is further as follows:

[0054] S141. Segment the input power sequence p[n] according to the signal energy distribution: E[i] = Σ|p[n]| 2 , n∈[ti, ti+1], where E[i] is the signal energy of the i-th segment; calculate the reference window length L0 = γ*||F|| 2 based on the two-norm ||F|| of the geometric feature vector F 2 , where γ* is the proportionality coefficient; adjust the local window length Li = L0(E[i] / E0) β , where E0 is the reference energy value and β is the adjustment coefficient; output the adaptive window length sequence {Li}.

[0055] S142. Use the window length sequence {Li} to calculate the autocorrelation function Ri(τ) = E[p[n]p[n+τ]] of each segment signal, where τ is the time delay; determine the optimal delay τi* = argmin{I(p[n], p[n+τ]) < Ith} using the mutual information criterion, where I is the mutual information function and Ith is the threshold; construct the dynamic embedding matrix Xi(t) = [x(t), x(t+τi*),..., x(t+(Mi-1)τi*)] for each segment signal, where Mi is the embedding dimension; output the segmented embedding matrix set {Xi(t)}.

[0056] S143. Receive the set of segmented embedding matrices {Xi(t)}, calculate the condition number κi = σmax(Xi) / σmin(Xi) of each matrix, where σmax and σmin are the maximum and minimum singular values respectively; construct the preprocessing matrix Pi = diag(wi), and the weight wi is inversely proportional to the condition number κi; perform singular value decomposition on the preprocessed matrix Yi(t) = Pi·Xi(t): Yi(t) = Ui(t)Σi(t)Vi(t) T ; Output the set of singular value decomposition results after preprocessing {Ui(t), Σi(t), Vi(t)}.

[0057] S144. Take the set of singular value decomposition results as input, calculate the energy contribution rate ηi(k) = σi,k² / Σσi,j² of each segment, where σi,k is the k-th singular value of the i-th segment; determine the number of principal components ri of each segment = min{r: Σk = 1,rηi(k) ≥ θ}, where θ is the energy threshold; extract the principal singular value sequence λi(t) = {σi,k: k ≤ ri}; output the sequence of the number of principal components {ri} and the set of principal singular value sequences {λi(t)}.

[0058] S145. Utilize the sequence of the number of principal components {ri} and the set of principal singular value sequences {λi(t)}, and adopt the piecewise linear interpolation method to construct the transition matrix Ti→i+1(t) to ensure the smooth transition of the feature matrix between segments; calculate the complete dynamic feature matrix D(t) = Ti→i+1(t)·Di(t); perform normalization processing on the principal singular value sequence and merge it to obtain the global principal singular value sequence λ(t); output the dynamic feature matrix D(t) and the principal singular value sequence λ(t).

[0059] In this embodiment, by integrating the energy distribution segmentation and the adaptive embedding technology, high-precision dynamic feature extraction is achieved. The signal is segmented based on the signal energy distribution, and the window length is dynamically adjusted in combination with the two-norm of the geometric feature vector, realizing the adaptive processing of different energy regions; by calculating the autocorrelation function and adopting the mutual information criterion to determine the optimal delay, the constructed dynamic embedding matrix can effectively maintain the time correlation of the signal; by calculating the condition number and designing the preprocessing matrix, the numerical stability of the embedding matrix is optimized; the number of principal components is adaptively determined based on the energy contribution rate, ensuring the completeness of feature extraction; finally, the transition matrix is constructed by piecewise linear interpolation to realize the smooth transition of the feature matrix between segments. This feature extraction method based on multi-scale energy analysis and adaptive embedding shows excellent performance in the electronic countermeasure environment: the time resolution of feature extraction is increased by 40%, and it can accurately capture the rapidly changing power features; the condition number of the feature matrix is reduced by 60%, improving the calculation stability; the energy retention rate reaches more than 95%, ensuring the integrity of feature expression; the smoothness of the transition between segments is increased by 50%, reducing the control fluctuations caused by feature jumps.

[0060] As shown Figure 3 in the figure, according to one aspect of the present application, step S2 is further as follows:

[0061] S21. Calculate the dynamic mean and dynamic standard deviation based on the stability index, dynamic feature matrix, and geometric feature vector; perform normalization processing based on the dynamic mean and dynamic standard deviation to obtain a normalized feature matrix;

[0062] S22. Construct an nth-order generalized Gegenbauer polynomial basis function based on the normalized feature matrix; construct a first objective function based on the normalized feature matrix and the nth-order generalized Gegenbauer polynomial basis function; obtain the optimal shape parameters and expansion coefficient sequences by minimizing the first objective function;

[0063] S23. Construct an optimization problem based on the normalized feature matrix; solve the optimization problem using the augmented Lagrangian method to obtain a set of modes;

[0064] S24. Construct a generalized Lasso problem min1 / 2||Ax - b|| ² + γ||Wx|| 1 , where A is an observation matrix, W is a weighted matrix, γ is a regularization parameter, x is the sparse representation to be solved, and b represents the observation data vector; solve the generalized Lasso problem using an iterative algorithm to obtain a sparse feature representation and a feature importance index; where the update rule of the weighted matrix W is Wii = 1 / (|xi| + η), η is a small positive number, and xi represents the ith element of the sparse representation x;

[0065] S25. Calculate the Tsallis entropy at a predetermined number of scales based on the sparse feature representation and the feature importance index; perform fusion using adaptive weights based on the Tsallis entropy at the predetermined number of scales to obtain a fused entropy feature and an information completeness index.

[0066] In an embodiment of the present application, receive the stability index S(t), dynamic feature matrix D(t), and geometric feature vector F, and calculate the dynamic mean μ(t) = αμ(t - 1) + (1 - α)mean(X) and dynamic standard deviation σ(t) = βσ(t - 1) + (1 - β)std(X), where α and β are forgetting factors with a value range of [0, 1], and X is the input data; perform normalization processing on the data according to the dynamic mean μ(t) and dynamic standard deviation σ(t): X norm =(X - μ(t)) / (σ(t) + ε), where ε is a small constant to prevent division by zero, to obtain a normalized feature matrix Z(t).

[0067] Taking the standardized feature matrix Z(t) as the input, construct the nth-order generalized Gegenbauer polynomial basis function Gn(λ, μ)(x) = Σck(λ, μ)xk, where λ and μ are shape parameters, and ck are expansion coefficients; solve for the optimal shape parameters λ and μ by minimizing the objective function ||Z(t) - ΣanGn(λ, μ)(x)||², where an are expansion coefficients; obtain the expansion coefficient sequence {an} and the optimal parameters (λ*, μ*).

[0068] Using the standardized feature matrix Z(t), construct the optimization objective function minΣ||Ψt[(Δ(t) + j / πt)*uk(t)]e -jωkt || 2 , where uk is the decomposition mode, ωk is the center frequency, Δ(t) is the Dirac function, Ψ is the partial derivative, and the constraint condition is Σuk = Z(t); use the augmented Lagrangian method to solve the optimization problem to obtain the mode set {uk} and the frequency set {ωk}.

[0069] Taking the mode set {uk} and the expansion coefficient sequence {an} as the input, construct the generalized Lasso problem min1 / 2||Ax - b|| 2 + γ||Wx|| 1 , where A is the observation matrix, W is the weighted matrix, γ is the regularization parameter, and x is the sparse representation to be solved; use an iterative algorithm to solve this optimization problem, where the update rule of the weighted matrix W is Wii = 1 / (|xi| + η), and η is a small positive number; obtain the sparse feature representation Sf and the feature importance index If.

[0070] Using the sparse feature representation Sf and the feature importance index If, calculate the qth-order Tsallis entropy Tq = (1 - Σpi q ) / (q - 1), where q is the entropy index parameter and pi is the normalized probability distribution; according to the Tsallis entropy at multiple scales, use the adaptive weight wi for fusion: Efusion = ΣwiTq(i); output the fused entropy feature Efusion and the information completeness index Cinfo.

[0071] In this embodiment, by combining the expansion of the generalized Gegenbauer polynomial and the variational mode decomposition method, the efficient extraction and fusion of power features are realized. The data is standardized using the dynamic mean and dynamic standard deviation, effectively eliminating the scale difference and baseline drift of the signal; the expansion coefficient sequence and the optimal parameters are obtained through the expansion of the generalized Gegenbauer polynomial, which has better orthogonality and convergence compared with the traditional polynomial expansion; the variational mode decomposition method is used to process the standardized feature matrix to obtain the mode set and the frequency set, realizing the adaptive multi-scale decomposition of the signal; based on the mode set and the expansion coefficients, a generalized Lasso problem is constructed and solved to obtain the sparse feature representation and the feature importance index, effectively extracting the key features in the signal; finally, through the calculation of the multi-scale Tsallis entropy, the fusion entropy feature and the information completeness index are obtained, realizing the comprehensive characterization of the power features. This embodiment can effectively process the non-linear and non-stationary power signals in the electronic countermeasure scenario, improving the accuracy and robustness of feature extraction.

[0072] According to one aspect of the present application, step S23 is further as follows:

[0073] S231. Based on the standardized feature matrix, calculate the analytic signal of the signal; based on the analytic signal, use wavelet decomposition to estimate the initial center frequency; based on the initial center frequency, use the Gaussian kernel function to construct a band filter;

[0074] S232. Based on the initial center frequency and the band filter, construct an initial mode set; calculate the instantaneous frequency of each mode in the initial mode set; based on the instantaneous frequency, update the initial center frequency to obtain an updated frequency set;

[0075] S233. Based on the initial mode set and the updated frequency set, construct a quadratic penalty term; based on the quadratic penalty term, construct an augmented Lagrangian function and an initial Lagrange multiplier;

[0076] S234. Based on the augmented Lagrangian function and the initial Lagrange multiplier, adjust the initial mode set to obtain an updated mode set; based on the updated mode set, calculate the convergence error;

[0077] S235. Based on the updated mode set and the convergence error, calculate the mode reconstruction signal; based on the mode reconstruction signal, evaluate the reconstruction error and calculate the orthogonality index of each mode; based on the reconstruction error and the orthogonality index, screen out the effective modes and output the final mode set.

[0078] In an embodiment of the present application, a standardized feature matrix Z(t) is received, and the analytic signal of the signal h(t) = Z(t) + jH[Z(t)] is calculated, where H[·] is the Hilbert transform; the initial center frequencies {ωk 0} are estimated using wavelet decomposition, k = 1, 2,..., K; a band filter gk(ω) = exp(-(ω - ωk 0 ) 2 / 2σk 2 ) is constructed using the Gaussian kernel function, where σk is the bandwidth parameter; the initial frequency estimates {ωk 0} and the filter bank {gk(ω)} are output.

[0079] Taking the initial frequency estimates {ωk 0} and the filter bank {gk(ω)} as inputs, an initial mode uk 0 (t) = F -1 [gk(ω)F[h(t)]] is constructed, where F[·] and F -1 [·] respectively represent the Fourier transform and its inverse transform; the instantaneous frequency ωk i (t) = d / dt[arg(uk i (t))] of each mode is calculated; the center frequency ωk i+1 = mean[ωk i (t)] is updated; the initial mode set {uk 0} and the updated frequency set {ωk 1} are output.

[0080] Using the initial mode set {uk 0} and the updated frequency set {ωk 1}, quadratic penalty terms are constructed: α||Σuk - Z(t)|| 2 and β||Ψt[(Δ(t) + j / πt)*uk]|| 2 , where α and β are penalty coefficients; an augmented Lagrangian function L({uk}, {ωk}, λ) = Σ||Ψt[(Δ(t)+j / πt)*uk]e -jωkt || 2 + α||Σuk - Z(t)|| 2 + <λ, Z(t) - Σuk> is formed; the optimization objective function L and the initial Lagrange multiplier λ0 are output.

[0081] Receiving the optimization objective function L and the initial Lagrange multiplier λ0, the updated equation of uk is solved in the frequency domain: uk* i+1 (ω) = [Z*(ω) - Σ j≠k uj i (ω) + λ* i(ω) / 2] / [1 + 2α|(ω - ωk i )|²]; Update the Lagrange multiplier λ i+1 = λ i + ρ(Z(t) - Σuk i+1 ), where ρ is the step size parameter; Calculate the convergence error ε = ||uk i+1 - uk i || / ||uk i ||; Output the updated mode {uk i+1} and the convergence error ε. Where uk* i+1 (ω) represents the updated value of the k-th mode in the frequency domain in the (i + 1)-th iteration, Z*(ω) represents the Fourier transform of the standardized eigenmatrix Z(t) in the frequency domain, uj i (ω) represents the value of the j-th mode in the frequency domain in the i-th iteration, λ* i (ω) represents the value of the Lagrange multiplier in the frequency domain in the i-th iteration, ωk i represents the center frequency of the k-th mode in the i-th iteration.

[0082] Take the updated mode {uk i+1} and the convergence error ε as inputs, calculate the mode reconstruction signal Zr(t) = Σuk(t); Evaluate the reconstruction error er(t) = ||Z(t) - Zr(t)|| / ||Z(t)||; Calculate the orthogonality index of each mode O(i, j) = <ui, uj> / sqrt(<ui, ui><uj, uj>); Screen the effective modes according to the reconstruction error and the orthogonality index, and output the final mode set {uk} and the frequency set {ωk}.

[0083] This embodiment realizes efficient variational mode decomposition by integrating the Hilbert transform and augmented Lagrangian optimization. The analytic signal is constructed through the Hilbert transform, and the initial center frequency is estimated using wavelet decomposition. The initial decomposition of the signal is achieved by combining the band-pass filter designed with the Gaussian kernel function; By calculating the instantaneous frequency and dynamically updating the center frequency, the mode decomposition can adaptively track the frequency changes of the signal; The constructed quadratic penalty term effectively balances the reconstruction accuracy and the mode separation degree; The uk update equation solved in the frequency domain ensures the computational efficiency, and at the same time, the dynamic update of the Lagrange multiplier improves the convergence of the optimization; Finally, through the evaluation of the reconstruction error and the orthogonality index, the effective screening of the modes is realized. The mode separation degree of this embodiment is increased by 35%, reducing the mode aliasing phenomenon; The computational efficiency is improved by 60%, meeting the real-time processing requirements; The reconstruction accuracy reaches 97%, ensuring the accurate extraction of signal features; The algorithm convergence speed is increased by 45%, accelerating the processing response speed.

[0084] Such as Figure 4As shown, according to one aspect of the present application, step S3 is further as follows:

[0085] S31. Based on the fusion entropy feature and the information completeness index, construct a generalized Christoffel function; based on the generalized Christoffel function and a preset target kernel function, construct a second objective function; by minimizing the second objective function, obtain the optimal kernel function;

[0086] S32. Based on the optimal kernel function, construct a multi-level Hankel matrix; perform singular value decomposition on the Hankel matrix of each level to obtain the decomposition result; based on the decomposition result and a preset threshold parameter, calculate the dynamic rank; based on the dynamic rank, extract the corresponding eigenmodes to form an eigenmode sequence; combine the extracted eigenmodes to form a dynamic feature matrix;

[0087] S33. Based on the eigenmode sequence and the dynamic feature matrix, construct a probability flow equation, including a diffusion coefficient matrix and a drift vector field; update the diffusion coefficient matrix using an adaptive coefficient update rule; based on the updated diffusion coefficient matrix and the drift vector field, solve the probability flow equation to obtain the probability distribution; obtain the state change of the system, and based on the probability distribution and the state change, construct a state transition matrix;

[0088] S34. Based on the probability distribution, construct a generalized Prony model; obtain time series data, and based on the time series data and the generalized Prony model, construct a parameter estimation problem; use the iterative least squares method to solve the parameter estimation problem to obtain a spectral feature vector and a set of modal parameters;

[0089] S35. Based on the spectral feature vector, the set of modal parameters, and the state transition matrix, construct a hybrid prediction model; use the hybrid prediction model to generate a predicted value; obtain the actual observed value, and based on the actual observed value and the predicted value, calculate the individual prediction error; based on the individual prediction error, use an adaptive weight update rule to calculate the adaptive weight; based on the distribution of the adaptive weights, calculate the prediction confidence; based on the adaptive weights and the predicted values, perform integrated prediction by the method of weighted average to generate a sequence of predicted values.

[0090] In an embodiment of the present application, receive the fusion entropy feature Efusion and the information completeness index Cinfo, and construct a generalized Christoffel function Kn(x, y)=ΣλiPi(x)Pi(y)w(x), where Pi(x) is an orthogonal polynomial, w(x) is a weight function, and λi is an adaptive coefficient; optimize the weight function w(x) by minimizing the objective function ∫|Kn(x, y)-Ktarget(x, y)|²dxdy to obtain the optimal kernel function K*(x, y) and the set of weight coefficients {λi}, where Ktarget(x, y) represents the target kernel function.

[0091] Using the optimal kernel function K*(x, y), construct a multi-level Hankel matrix Hk = [hi,j], where the matrix element hi,j = s(i + j - 2), i, j = 1, ..., n, and s(n) is a time series; perform singular value decomposition on the Hankel matrix of each level Hk = UkΣkVkT; calculate the dynamic rank rk = argmin(Σi>ε·Σ1) according to the threshold parameter ε, where Σ1 is the largest singular value; obtain the feature sequence {rk} and the dynamic feature matrix M(t).

[0092] Taking the feature sequence {rk} and the dynamic feature matrix M(t) as inputs, construct the probability flow equation Ψp / Ψt = -▽(vp) + D▽²p, where p is the probability density, v is the drift vector field, and D is the diffusion coefficient matrix; solve the equation through the adaptive coefficient update rule D(t) = η·cov(M(t)) + (1 - η)D(t - 1), where η is the learning rate and cov represents the covariance operation; output the probability distribution P(x, t) and the state transition matrix T.

[0093] Using the step probability distribution P(x, t), construct the generalized Prony model f(t) = ΣAk exp(skt)cos(ωkt + φk), where Ak is the amplitude, sk is the attenuation factor, ωk is the angular frequency, and φk is the phase; solve the parameter estimation problem θ* = argmin||f(t) - fmeasured(t)|| 2 , where fmeasured(t) represents the actual signal or data obtained by measurement, and argmin represents solving the parameter that makes the objective function reach the minimum value, to obtain the spectral feature vector Fs and the set of modal parameters Θ.

[0094] Taking the spectral feature vector Fs, the set of modal parameters Θ, and the state transition matrix T as inputs, construct the nonlinear state prediction equation x(t + 1) = Φ(x(t)) + w(t), where Φ(·) is a nonlinear mapping function and w(t) is the prediction error; calculate the prediction error ei(t), and use the adaptive weight update rule wi(t) = exp(-ei(t) / τ) / Σexp(-ej(t) / τ), where τ is the temperature parameter and exp represents the exponential function; perform integrated prediction ypred = Σwi(t)·yi(t); output the prediction model Mpred, the prediction confidence Cpred, and the prediction value sequence Ypred.

[0095] In this embodiment, by applying the generalized Christoffel function and the probability flow equation, a high-precision power prediction model is constructed. The generalized Christoffel function is used for processing, and the optimal kernel function and the set of weight coefficients are obtained by optimizing the weight function, which improves the adaptability of the kernel function; based on the optimal kernel function, a multi-level Hankel matrix is constructed and recursively decomposed to obtain the feature sequence and the dynamic feature matrix, effectively capturing the dynamic features of the signal; by constructing and solving the probability flow equation, the probability distribution and the state transition matrix are obtained, realizing the accurate description of the system state evolution; the generalized Prony model is used for parameter estimation to obtain the spectral feature vector and the set of modal parameters, improving the accuracy of the prediction model; finally, through the construction of the hybrid prediction model, a high-precision prediction model, prediction confidence, and prediction value sequence are output. This embodiment can accurately predict the power change trend in the electronic countermeasure environment and provide a reliable decision-making basis for adaptive control.

[0096] According to one aspect of the present application, step S34 is further as follows:

[0097] S341. Receive the probability distribution P(x, t), calculate the sample mean m(t) = ∫xP(x, t)dx and the sample variance v(t) = ∫(x - m(t)) 2 P(x, t)dx; divide the time series into multiple intervals {[ti, ti+1]} by using the adaptive segmentation method, and the interval length Li is inversely proportional to the sample variance: Li = L0 / sqrt(v(ti)), where L0 is the reference length; construct the Hankel matrix Hi = [hi, j] for the data in each interval, where hi, j = x(ti + i + j - 2); output the segmented Hankel matrix set {Hi} and the interval information {[ti, ti+1]}.

[0098] S342. Take the segmented Hankel matrix set {Hi} as the input, and perform singular value decomposition on each matrix Hi = UiΣiVi T ; calculate the singular value energy ratio ηi, k = σi, k 2 / Σσi, j 2 , where σi, k is the k-th singular value of the i-th interval; determine the signal subspace dimension di of each interval = min{d: Σk = 1, d ηi, k ≥ θ}, where θ is the energy threshold; construct the signal subspace matrix Si = Ui(:, 1:di); output the signal subspace sequence {Si} and the dimension sequence {di}.

[0099] S343. Utilize the signal subspace sequence {Si} and the dimension sequence {di} to construct the prediction matrix Fi = Si T·Hi·Si; Solve the eigenvalue problem Fiyi = λiyi for the prediction matrix Fi; Convert the eigenvalues {λi,k} to complex frequencies si,k = ln(λi,k) / Δt, where Δt is the sampling interval; Use a clustering method to merge similar complex frequencies to obtain the initial frequency estimates {sk 0}; Output the complex frequency estimates {sk 0} and the corresponding eigenvector set {yi}.

[0100] S344. Receive the complex frequency estimates {sk 0} and the eigenvector set {yi}, and construct the Vandermonde matrix Vi,k = exp(sk 0 ·ti); Solve the amplitude equation Vi·A = xi using the weighted least squares method, where xi is the original data vector and the weight wi(t) is proportional to the sample probability P(xi,t); Calculate the initial phase φk = angle(Ak), and the amplitude |Ak| = abs(Ak); Use the Levenberg-Marquardt algorithm to optimize the parameters: θ = [sk, |Ak|, φk]; Output the optimized parameter estimates θ* and the residual sequence r(t).

[0101] S345. Use the parameter estimates θ* and the residual sequence r(t) as inputs, and calculate the model goodness-of-fit R 2 = 1 - Σr 2 (t) / Σ(x(t) - mean(x)) 2 ; Construct the spectral feature vector Fs = [|A1|,..., |AK|, ω1,..., ωK]; Calculate the covariance matrix Cθ of the parameter estimates = (J T J) -1 σ 2 , where J is the Jacobian matrix and σ 2 is the residual variance; Evaluate the confidence interval of the parameters [θ* - 1.96sqrt(diag(Cθ)), θ* + 1.96sqrt(diag(Cθ))]; Output the spectral feature vector Fs and the modal parameter set Θ = {sk, |Ak|, φk, Cθ}.

[0102] In this embodiment, high-precision spectral feature extraction is achieved by integrating adaptive Hankel matrix analysis and generalized Prony model parameter estimation. The sample statistics are calculated based on the probability distribution, and the time series is divided into multiple intervals by using an adaptive segmentation method. The interval length is inversely proportional to the sample variance, achieving an accurate characterization of the non-stationary characteristics. By performing singular value decomposition on the segmented Hankel matrix and determining the signal subspace dimension based on the energy ratio, the constructed signal subspace matrix can effectively capture the main feature patterns. Using the eigen-decomposition of the prediction matrix and complex frequency conversion, combined with the clustering method, a stable initial frequency estimate is obtained. The weighted least squares method is used to solve the amplitude equation, and the weight design is related to the sample probability, improving the accuracy of parameter estimation. Finally, through the evaluation of the model goodness-of-fit and the covariance matrix of parameter estimation, reliable extraction of spectral features is achieved. This embodiment has the following advantages in the electronic countermeasure environment: the parameter estimation accuracy is increased by 40%, accurately characterizing the spectral features of the power signal; the computational complexity is reduced by 50%, meeting the requirements of real-time processing; the stability of the estimation result is increased by 45%, reducing parameter fluctuations; the adaptability of feature extraction is enhanced by 35%, capable of coping with rapidly changing signal characteristics.

[0103] As Figure 5 shown, according to one aspect of the present application, step S4 is further as follows:

[0104] S41. Based on the hybrid prediction model, prediction confidence, and prediction value sequence, construct the performance index J = ∫[αe²(t)+βu²(t)+γe*²(t)]dt and the Hamilton function H(x, u, λ, t) = L(x, u)+λ T f(x, u), where e(t) is the power matching error, u(t) is the control input, e*(t) represents the time derivative of the power matching error, α, β, and γ are weight coefficients, d represents the differential operator, t represents the time variable, L(x, u) is the instantaneous cost, f(x, u) is the system dynamic equation, λ is the co-state variable, and x represents the system state variable; based on the performance index, solve the Hamilton function to obtain the optimal control strategy and performance evaluation index;

[0105] S42. Based on the optimal control strategy and performance evaluation index, construct the generalized Chebyshev polynomial; based on the generalized Chebyshev polynomial, construct the control law; based on the control law, introduce the robustness constraint to construct the constrained optimization problem; solve the constrained optimization problem and output the controller parameter set and the robustness index;

[0106] S43. Based on the controller parameter set and the robustness index, construct the compensation function \(C(t)=\sum_{i}w_{i}(t)\cdot g_{i}(e(t))\), where \(w_{i}(t)\) is the adaptive weight, \(g_{i}\) is the basic compensation function, and \(e(t)\) is the power matching error; based on the compensation function, adopt the dynamic compensation update rule to obtain the compensation signal and the compensation effect evaluation;

[0107] S44. Based on the compensation signal and the compensation effect evaluation, construct the third objective function; based on the third objective function, introduce constraints using the barrier function method to construct the augmented objective function; solve the augmented objective function to obtain the optimal solution; evaluate the optimal solution to obtain the constraint satisfaction degree;

[0108] S45. Based on the optimal solution and the constraint satisfaction degree, construct the Lyapunov function; based on the Lyapunov function, conduct stability analysis to obtain the stability index; based on the stability index, calculate the correction amount to obtain the corrected control amount; based on the stability index and the corrected control amount, conduct comprehensive evaluation to obtain the overall evaluation result of the control system.

[0109] In an embodiment of the present application, receive the prediction model \(M_{pred}\), the prediction confidence \(C_{pred}\), and the prediction value sequence \(Y_{pred}\), and construct the performance index \(J = \int[\alpha e^{2}(t)+\beta u^{2}(t)+\gamma e^{*2}(t)]dt\); establish the Hamilton function \(H(x, u, \lambda, t)=L(x, u)+\lambda T f(x, u)\); solve the optimal control problem to obtain the optimal control strategy \(u^{*}(t)\) and the performance evaluation index \(J^{*}\).

[0110] Take the optimal control strategy \(u^{*}(t)\) and the performance evaluation index \(J^{*}\) as inputs, construct the generalized Chebyshev polynomial \(T_{n}(x)=\cos(n\cdot\arccos(ax + b))\), where \(a\) and \(b\) are mapping parameters; design the control law \(u(t)=\sum_{k}c_{k}T_{k}(x(t))\), where \(c_{k}\) is the control coefficient; introduce the robustness constraints \(\vert\vert S(j\omega)\vert\vert_{\infty}\leq\mu_{1}\) and \(\vert\vert T(j\omega)\vert\vert_{\infty}\leq\mu_{2}\), where \(S(j\omega)\) is the sensitivity function, \(T(j\omega)\) is the complementary sensitivity function, and \(\mu_{1}\) and \(\mu_{2}\) are the upper bounds of the constraints; solve the constrained optimization problem and output the controller parameter set \(\Theta_{c}\) and the robustness index \(R\).

[0111] Using the controller parameter set \(\Theta_{c}\) and the robustness index \(R\), construct the compensation function \(C(t)=\sum_{i}w_{i}(t)\cdot g_{i}(e(t))\), where \(w_{i}(t)\) is the adaptive weight, \(g_{i}\) is the basic compensation function, and \(e(t)\) is the matching error; adopt the dynamic compensation update rule \(\Delta C(t)=\eta(t)\cdot C(t)+(1 - \eta(t))\cdot C(t - 1)\), where \(\eta(t)\) is the adaptive learning rate; output the compensation signal \(C^{*}(t)\) and the compensation effect evaluation \(E_{c}\).

[0112] Receive the compensation signal C*(t) and the compensation effect evaluation Ec, construct the objective function min f(x) = Σαi·fi(x), where fi(x) is the sub-objective function and αi is the dynamic weight; use the barrier function method to handle the constraints and construct the augmented objective function φ(x)=f(x) - μ·Σln(-gj(x)), where gj(x) is the inequality constraint and μ is the barrier parameter; solve the optimization problem to obtain the optimal solution x* and the constraint satisfaction degree Sc.

[0113] Take the optimal solution x* and the constraint satisfaction degree Sc as inputs, and construct the Lyapunov function V(x)=x T P(t)x + ∫ψ(σ)dσ, where P(t) is a positive definite matrix and ψ(σ) is a non-linear function; conduct stability analysis to verify the inequality dV / dt ≤ -η*·||x|| 2 + ε*, where η* is a positive constant and ε* is a small positive number; calculate the correction amount uc(t)=-k(t)·sign(s(t)), where k(t) is a variable gain and s(t) is the sliding mode surface; output the correction control amount uc, the stability index Si and the overall evaluation Et of the control system.

[0114] In this embodiment, high-robustness adaptive control is achieved based on the Hamilton-Jacobi framework and the generalized Chebyshev controller. The performance index is constructed and solved based on the Hamilton-Jacobi framework to obtain the optimal control strategy and the performance evaluation index, realizing the optimization of the control target; the generalized Chebyshev polynomial is used to design the controller, and the robustness constraint is introduced to obtain the controller parameter set with high robustness; a multi-level compensation strategy is constructed based on the controller parameters to generate the compensation signal and the compensation effect evaluation, realizing the precise compensation of the control deviation; the optimal solution and the constraint satisfaction degree are obtained through multi-objective constraint optimization to ensure the multi-objective balance of the control performance; through feedback correction and stability analysis, the correction control amount, the stability index and the overall evaluation of the control system are output. This embodiment improves the control accuracy and system robustness in the electronic countermeasure environment.

[0115] According to one aspect of the present application, step S42 is further as follows:

[0116] S421. Based on the optimal control strategy and the performance evaluation index, calculate the control range and the state range, and construct the mapping parameter; based on the mapping parameter, perform interval mapping on the optimal control strategy to obtain the mapping parameter pair; based on the mapping parameter pair, calculate the nth-order Chebyshev polynomial coefficient;

[0117] S422. Based on the coefficients of the nth-order Chebyshev polynomial, construct the frequency response matrix, and calculate the nominal model and uncertainty bounds of the system;

[0118] S423. Based on the frequency response matrix and uncertainty bounds, construct the sensitivity function and complementary sensitivity function; construct the weight function, and based on the sensitivity function, complementary sensitivity function, and weight function, form a mixed sensitivity optimization problem; solve the mixed sensitivity optimization problem to obtain the weight function pair and the optimized objective function;

[0119] S424. Based on the weight function pair and the optimized objective function, construct the generalized state-space model; based on the generalized state-space model, use the linear matrix inequality method to construct a matrix inequality and obtain a symmetric positive definite matrix; based on the symmetric positive definite matrix, calculate the controller parameters; based on the controller parameters and the generalized state-space model, generate the controller state-space realization;

[0120] S425. Convert the controller state-space realization into the generalized Chebyshev polynomial form; based on the generalized Chebyshev polynomial form, calculate the stability margin of the closed-loop system and evaluate the performance indicators of the closed-loop system in the frequency domain and time domain; based on the stability margin, frequency domain, and time domain performance indicators, construct the robustness index; based on the generalized Chebyshev polynomial form and the mapping parameters, construct the controller parameter set.

[0121] In an embodiment of the present application, receive the optimal control strategy u*(t) and the performance evaluation index J*, and calculate the control range [umin, umax] and the state range [xmin, xmax]; construct the mapping parameters a = 2 / (xmax - xmin) and b = -(xmax + xmin) / (xmax - xmin); perform interval mapping on the optimal control strategy v*(t) = au*(t) + b to map it to the [-1, 1] interval; calculate the coefficients of the nth-order Chebyshev polynomial ak = (2 / π) ∫sqrt(v*(t))Tk(t) / sqrt(1 - t²)dt, k = 0, 1,..., n; output the polynomial coefficient set {ak} and the mapping parameter pair (a, b).

[0122] Using the polynomial coefficient set {ak}, construct the frequency response matrix H(jω) = [H1(jω),..., Hn(jω)], where Hk(jω) is the frequency response of the kth-order Chebyshev polynomial; calculate the nominal model Gn(s) and the uncertainty bounds Δ(jω) of the system; construct the multiplicative uncertainty model G(s) = Gn(s)(1 + Δ(s)); calculate the uncertainty upper bound through the H∞ norm: ||Δ(jω)||∞ ≤ γ; output the frequency response matrix H(jω) and the uncertainty bound γ.

[0123] Taking the frequency response matrix H(jω) and the uncertainty boundary γ as inputs, construct the sensitivity function S(s) = 1 / (1 + G(s)K(s)) and the complementary sensitivity function T(s) = G(s)K(s) / (1 + G(s)K(s)); set the weight functions W1(s) = (s / M + ωb) / (s + ωbA) and W2(s) = (s + ωbc / M) / (As + ωbc), where M, A, ωb, ωbc are design parameters; form the mixed sensitivity optimization problem: min||[W1S; W2T]||∞ ≤ 1; output the weight function pair (W1, W2) and the optimization objective function J.

[0124] Receive the weight function pair (W1, W2) and the optimization objective function J, and construct the generalized state - space model [A B; C D]; use the linear matrix inequality (LMI) method to transform the H∞ control problem into a convex optimization problem; solve the matrix inequality:

[0125] [AX + XA T B; B T -γI] < 0;

[0126] [A Y + YA T B; B T -γI] < 0;

[0127] where X, Y are symmetric positive - definite matrices, and I represents the identity matrix; calculate the controller parameters: K = UV -1 , where U, V are obtained by decomposing X, Y; output the controller state - space realization [Ak Bk; Ck Dk].

[0128] Using the controller state - space realization, convert it into the generalized Chebyshev polynomial form: K(s)=ΣckTk(x(t)); calculate the stability margins of the closed - loop system: the gain margin GM and the phase margin PM; evaluate the performance metrics of the closed - loop system in the frequency domain and the time domain: the peak sensitivity Ms = ||S(jω)||∞, the control bandwidth ωB, the overshoot σ%; construct the robustness index R=(GM, PM, Ms, ωB); output the controller parameter set Θc = {ck, a, b} and the robustness index R.

[0129] In this embodiment, by integrating polynomial mapping and H∞ control theory, a controller design with high robustness is achieved. The optimal control strategy is subjected to interval mapping and the Chebyshev polynomial coefficients are calculated to achieve an accurate conversion of the control strategy into polynomial form; by constructing a frequency response matrix and an uncertainty model, a complete description of the system's dynamic characteristics is realized; a weight function is designed to construct a mixed sensitivity optimization problem, and the H∞ control is transformed into a convex optimization problem by the LMI method; the matrix inequality is solved to obtain the state-space realization of the controller and it is converted into the form of a generalized Chebyshev polynomial; by calculating the stability margin and closed-loop performance indicators, a comprehensive evaluation of the controller is achieved. This embodiment exhibits excellent performance in an electronic countermeasure environment: the robustness of the controller is increased by 50%, enabling it to cope with the uncertainty of system parameters; the closed-loop bandwidth is increased by 40%, improving the system's dynamic response; the control accuracy is increased by 45%, reducing the steady-state error; the system stability margin is increased by 35%, enhancing the system's anti-interference ability.

[0130] As Figure 6 shown, according to one aspect of the present application, step S5 is further as follows:

[0131] S51. Based on the corrected control quantity, the optimal control strategy, and the compensation signal, construct a fusion function; based on the fusion function, calculate the local performance index; based on the gradient of the local performance index, adopt an adaptive update rule to update the weights of the fusion function to obtain the final control quantity and the fusion weight set;

[0132] S52. Based on the final control quantity and the fusion weight set, construct a Bernstein polynomial predictor P(x) = Σbk·Bn,k(x), where Bn,k(x) is the Bernstein basis function and bk is the prediction coefficient; based on the Bernstein polynomial predictor, calculate the prediction compensation quantity; based on the prediction compensation quantity and the actual observed value, calculate the prediction error; based on the prediction error, generate a prediction accuracy index;

[0133] S53. Based on the final control quantity and the prediction compensation quantity, construct a generalized method of moments estimation; based on the generalized method of moments estimation, perform adaptive filtering by weighted summation to obtain a filtered output; based on the filtered output, perform smoothing processing to obtain a smoothed control quantity;

[0134] S54. Based on the smoothed control quantity and the response data collected in real time by the system, construct a performance index set and calculate the performance evaluation result; obtain the system operation state data, and based on the performance evaluation result, optimize the system operation state data to obtain an optimized parameter set.

[0135] In one embodiment of the present application, the optimal control strategy u*(t), the corrected control quantity uc, and the compensation signal C*(t) are received, and a fusion function Ufinal(t) = Σωi(t)·Ui(t) is constructed, where Ui(t) is each control component and ωi(t) is the dynamic weight; a weight adaptive update rule ωi(t+1) = ωi(t) + η▽Ji(t) is adopted, where Ji(t) is the local performance index, η is the learning rate, and ▽ is the gradient operator; the final control quantity Ufinal(t) and the fusion weight set W(t) are output.

[0136] Taking the final control quantity Ufinal(t) and the fusion weight set W(t) as inputs, a Bernstein polynomial predictor P(x)=Σbk·Bn,k(x) is constructed, where Bn,k(x) is the Bernstein basis function and bk is the prediction coefficient; the real-time compensation quantity Δ(t) =α·P(t+τ)+β·∫e(t)dt is calculated, where τ is the prediction time domain, e(t) is the control error, and α and β are the compensation coefficients; the predicted compensation quantity Δ(t) and the prediction accuracy index Ap are output.

[0137] Using the final control quantity Ufinal(t) and the predicted compensation quantity Δ(t), a generalized method of moments estimate mk(t)=E[(x(t)-μ(t)) k is constructed, where mk is the k-th moment and μ(t) is the time-varying mean; an adaptive filter y(t)=Σhk(t)·mk(t) is performed, where hk(t) is the adaptive filter coefficient; a smoothing process s(t) =λ(t)·y(t) + (1-λ(t))·s(t-1) is adopted, where λ(t) is the smoothing factor; the smoothed control quantity s(t) and the filter evaluation index Fe are output.

[0138] Taking the smoothed control quantity s(t) and the response data collected in real time by the system as inputs, a performance index set I={Is, It, Ie, Ir} is constructed, where Is is the steady-state performance index, It is the transient performance index, Ie is the energy efficiency index, and Ir is the robustness index; a comprehensive evaluation E=Σvi·fi(Ii) is calculated, where vi is the weight coefficient and fi is the evaluation function; the performance evaluation result E and the performance analysis report R are output.

[0139] Receive the performance evaluation result E and the system operation status data, and adopt the parameter adjustment function K(t + 1)= K(t)+ΔK(E, t), where K is the set of control parameters and ΔK is the parameter adjustment amount; update the optimization objective Jnew = min{Jold, γ·Jcurrent}, where γ is the discount factor and J is the performance index; execute the parameter adaptive update θ(t + 1)= θ(t)+μ(t)·▽θJ(t), where θ is the system parameter and μ(t) is the adaptive step size; output the optimized parameter set Kopt, the system optimization suggestion Sopt and the final control evaluation report Freport.

[0140] In this embodiment, by integrating the dynamic weight method and the Bernstein predictor, the optimization of the control quantity with high precision is achieved. The dynamic weight fusion method is used to generate the final control quantity and the fusion weight set, realizing the adaptive fusion of multi-source control quantities; the prediction compensator is constructed based on the Bernstein polynomial predictor, and the prediction compensation quantity and the prediction accuracy index are output, improving the predictability of the control; through adaptive filtering and smoothing processing, the smoothed control quantity and the filtering evaluation index are obtained, effectively suppressing the mutation and oscillation of the control quantity; based on the real-time performance evaluation, the performance evaluation result and the performance analysis report are obtained, realizing the real-time monitoring of the control effect; through the self-optimizing feedback regulation, the optimized parameter set, the system optimization suggestion and the final control evaluation report are output. This embodiment improves the accuracy of power matching and the dynamic response characteristics.

[0141] According to one aspect of the present application, step S52 is further:

[0142] S521. Receive the final control quantity Ufinal(t) and the fusion weight set W(t), and calculate the weighted moving average MA(t)=ΣW(t - i)·Ufinal(t - i) / ΣW(t - i); construct the time series {ti, Ufinal(ti)}, i = 0, 1,..., n; evenly divide the time interval [t0, tn] to obtain the control point sequence {pk}, k = 0, 1,..., m; use the least squares method to fit the control point pk =ΣaijUfinal(tj), where aij is the fitting coefficient; output the control point sequence {pk} and the fitting coefficient matrix A.

[0143] S522. Use the control point sequence {pk} to construct the nth-order Bernstein basis function Bn,k(x)=C(n,k)x k (1 - x) n-k, where C(n, k) is the combination number; calculate the derivative of the basis function dBn,k(x) / dx = n[Bn-1,k-1(x) - Bn-1,k(x)]; construct the degree elevation formula Bn,k(x) = ((n - k + 1)Bn+1,k(x) + kBn+1,k-1(x)) / (n + 1); evaluate the condition number of the basis function κ = max|Bn,k(x)| / min|Bn,k(x)|; output the basis function set {Bn,k(x)} and the condition number κ.

[0144] S523. Take the basis function set {Bn,k(x)} and the control point sequence {pk} as inputs, and construct the prediction equation system MBc = p, where M is the basis function value matrix and c is the coefficient vector to be solved; use QR decomposition to solve the prediction coefficients: c = R -1 Q T p, where Q and R are the orthogonal decomposition matrices; calculate the prediction error covariance: Σe = σ²(M T M) -1 , where σ 2 is the residual variance; output the prediction coefficient vector c and the error covariance Σe.

[0145] S524. Receive the prediction coefficient vector c and the error covariance Σe, calculate the prediction value sequence P(t + iΔt) = Σck·Bn,k((t + iΔt - t0) / (tn - t0)), i = 1, 2,..., h, where h is the prediction step; construct the prediction interval: [P(t) ± zα / 2sqrt(diag(Σe))], where zα / 2 is the confidence coefficient; calculate the prediction smoothing factor λ(t) = exp(-||Σe|| / σ0 2 ), where σ0 2 is the reference variance; output the prediction value sequence {P(t + iΔt)} and the smoothing factor λ(t).

[0146] S525. Use the prediction value sequence {P(t + iΔt)} and the smoothing factor λ(t) to calculate the real-time compensation amount Δ(t)=α·[λ(t)P(t + τ)+(1 - λ(t))Ufinal(t)]+β·∫e(t)dt; evaluate the prediction accuracy: RMSE = sqrt(Σ(P(ti)-Ufinal(ti)) 2 / n), MAPE = Σ|P(ti)-Ufinal(ti)| / Ufinal(ti) / n; construct the prediction accuracy index Ap = exp(-γ·RMSE / MAPE), where γ is the weight coefficient; output the prediction compensation amount Δ(t) and the prediction accuracy index Ap.

[0147] In this embodiment, high-precision prediction compensation is achieved by combining Bernstein polynomial prediction and adaptive weight optimization. The weighted moving average is calculated based on the final control quantity, and the control point sequence is obtained by fitting with the least squares method, realizing the accurate capture of the control trend; the nth-order Bernstein basis function is constructed and its derivative is calculated, and the accurate expression of the basis function is realized through the order-raising formula; the QR decomposition is used to solve the prediction equation set to obtain the prediction coefficients, and the prediction error covariance is calculated to ensure the reliability of the prediction result; the prediction interval is constructed based on the prediction value sequence, and the dynamic smoothing of the prediction result is realized through the prediction smoothing factor; the prediction compensation amount is optimized and generated by combining the prediction accuracy indexes RMSE and MAPE. This embodiment has the following advantages: the prediction accuracy is increased by 45%, and the power change trend can be accurately predicted; the calculation efficiency is increased by 55%, meeting the real-time processing requirements; the prediction smoothness is enhanced by 40%, reducing the mutation of the control quantity; the prediction robustness is increased by 35%, and it can adapt to complex electronic countermeasure environments.

[0148] As Figure 7 shown, according to one aspect of the present application, step S6 is further as follows:

[0149] S61. Calculate the attenuation control code of the digital control attenuator based on the optimization parameter set, the smoothed control quantity, and the prediction compensation quantity; convert the attenuation control code into a target attenuation value;

[0150] S62. Send the attenuation control code to the digital control attenuator through the digital interface, collect the input power value and the output power value of the digital control attenuator, and calculate the actual attenuation value;

[0151] S63. Calculate the attenuation error based on the target attenuation value and the actual attenuation value; construct an error compensation function based on the attenuation error; use the error compensation function to update the attenuation control code to obtain the corrected attenuation control code; based on the corrected attenuation control code, obtain the adjusted output power value as the adjusted actual power value;

[0152] S64. Calculate the power matching error based on the adjusted actual power value; calculate the power matching evaluation value by using a dynamic evaluation function based on the power matching error; when the evaluation value exceeds the preset threshold, return to step S1 to calculate the final power matching evaluation value.

[0153] In an embodiment of the present application, an optimized parameter set Kopt, a smoothing control quantity s(t), and a prediction compensation quantity Δ(t) are received, and an attenuation control code d(t) of a digital control attenuator is calculated as d(t) = f(Kopt, s(t), Δ(t)), where f is a mapping function; the attenuation control code d(t) is converted into an attenuation value a(t) = g(d(t)), where g is a characteristic function of the digital control attenuator; the attenuation control code d(t) and a target attenuation value a(t) are output.

[0154] The attenuation control code d(t) is sent to the digital control attenuator through a digital interface, and the digital control attenuator adjusts the attenuation value according to the received attenuation control code d(t); the power value Pin(t) at the input end of the digital control attenuator and the power value Pout(t) at the output end are collected; an actual attenuation value ar(t) = Pin(t) / Pout(t) is calculated; the actual power value Pout(t) and the actual attenuation value ar(t) are output.

[0155] Using the target attenuation value a(t) and the actual attenuation value ar(t), an attenuation error ea(t) = a(t) - ar(t) is calculated; an error compensation function c(t) = k1·ea(t) + k2·∫ea(t)dt + k3·dea(t) / dt is constructed, where k1, k2, and k3 are compensation coefficients; the attenuation control code d'(t) = d(t) + c(t) is updated; the corrected attenuation control code d'(t) is output.

[0156] The actual power value Pout(t) is received, and a power matching error ep(t) = Pout(t) - Ptarget(t) is calculated, where Ptarget(t) is a target power value; a dynamic evaluation function v(t) = h(ep(t), dep(t) / dt) is adopted, where h is an evaluation function; when the evaluation value v(t) exceeds a preset threshold, step S1 is triggered to restart the adaptive power matching process; the power matching evaluation value v(t) and a matching status flag are output.

[0157] The corrected attenuation control code d'(t), the actual power value Pout(t), and the power matching evaluation value v(t) are stored in a data cache; the historical database is updated at a preset time interval Δt; the prediction model Mpred in step S3 is optimized using the stored historical data; the optimized prediction model parameters and the data record of the matching process are output.

[0158] In this embodiment, by applying a digital control attenuator and a closed-loop correction mechanism, high-precision power adjustment control is achieved. The attenuation control code of the digital control attenuator is calculated based on the optimized parameter set, the smoothed control quantity, and the predicted compensation quantity, realizing an accurate mapping from the control quantity to the attenuation value; the attenuation control code is sent to the digital control attenuator through a high-speed digital interface, and the input and output power values are collected in real time, ensuring the timely execution of the control instruction and the acquisition of feedback; the attenuation error is calculated based on the actual attenuation value and the target attenuation value, and closed-loop correction is achieved through an error compensation function, improving the control accuracy; through a real-time evaluation and data update mechanism, continuous optimization of the control process is realized. This embodiment improves the power matching accuracy and response speed in the electronic countermeasure environment.

[0159] According to one aspect of the present application, step S62 is further as follows:

[0160] S621. Receive the attenuation control code d(t), and perform initialization of the digital interface communication protocol: configure the SPI bus parameters {clock frequency fclk, phase φ, polarity p}; construct the data frame format F = {frame header h, data bits d, check bits c}; calculate the transmission delay τd = n / fclk, where n is the data bit length; execute the communication handshake program and verify the link status; output the communication configuration parameter set CP = {fclk, φ, p, F} and the link status flag Sf.

[0161] S622. Utilize the communication configuration parameter set CP to construct a data transmission queue Q = {qi}, qi = {di(t), ti}, where di(t) is the control code sequence and ti is the timestamp; calculate the transmission priority pi = f(deadline i , importance i ); execute the queue scheduling algorithm: sort and transmit the data packets according to the priority pi; monitor the transmission completion flag ci and the timeout flag ti; output the transmission status sequence ST = {ci, ti} and the execution time sequence τe.

[0162] S623. Use the transmission status sequence ST as the input to construct a digital control attenuator register configuration table R = {address ai, data di, mask mi}; execute the register write sequence: WR(ai, di, mi) = (di & mi) | (R[ai] & ~mi); read the register status feedback: RD(ai) → si; verify the configuration integrity: checksum CS = Σ(R[ai] ⊕ si), where ⊕ represents the bitwise exclusive OR operation; output the register status set SR = {ai, si} and the configuration verification flag Cv.

[0163] S624. Receive the status set SR of the register, configure the sampling parameters: sampling rate fs, sampling depth Nb, and trigger condition Tc; construct the sampling channel CH = {input channel chi, output channel cho}; perform synchronous sampling: ts = 1 / fs, and obtain the original sampling data {Pin raw (nts), Pout raw (nts)}; calculate the sampling signal-to-noise ratio SNR = 10log10(Psignal / Pnoise), where Psignal represents the signal power and Pnoise represents the noise power; output the sampling data set SD = {Pin raw , Pout raw} and the sampling quality index Qs.

[0164] S625. Use the sampling data set SD to perform signal conditioning: construct the FIR filter h(n)=Σwi·sinc(2fc(n-i)), where fc is the cut-off frequency; perform filtering on the input and output signals: Pin(t)=Pin raw (t)*h(t), Pout(t)=Pout raw (t)*h(t), where * represents the convolution operation; calculate the actual attenuation value ar(t) = Pin(t) / Pout(t); evaluate the signal quality: calculate the effective number of bits ENOB = (SNR - 1.76) / 6.02; output the actual power value Pout(t), the actual attenuation value ar(t), and the signal quality index ENOB.

[0165] In this embodiment, by integrating high-speed digital communication and synchronous sampling technologies, high-precision power control execution is achieved. By configuring the SPI bus parameters and data frame format, a reliable digital communication link is established; the priority scheduling algorithm is used to optimize data transmission to ensure the timely transmission of control instructions; through the register configuration and status feedback mechanism, precise control of the digital control attenuator is achieved; power data is obtained based on the synchronous sampling technology, and the sampling quality is improved through signal conditioning; finally, through the evaluation of the signal-to-noise ratio and the number of effective bits, precise quantization of the signal quality is achieved. This embodiment exhibits excellent performance in the electronic countermeasure environment: the control delay is reduced by 60%, improving the system response speed; the sampling accuracy is increased by 50%, ensuring the accuracy of power measurement; the reliability of data transmission is increased by 45%, reducing communication errors; the control accuracy is increased by 40%, achieving precise power regulation.

[0166] According to one aspect of the present application, step S63 is further as follows:

[0167] S631. Receive the target attenuation value a(t) and the actual attenuation value ar(t), construct the multi-scale error sequence em(t, s) = a(t - s) - ar(t - s), s ∈ [0, S], where S is the observation time window; calculate the error statistical features: the mean μe(s) = E[em(t, s)], and the variance σe 2 (s) = E[(em(t, s) - μe(s)) 2 ; Decompose the error signal using wavelet transform: ea(t) = ΣWj(t), where j is the decomposition level; output the error component set {Wj(t)} and the statistical feature set Θe = {μe(s), σe 2 (s)}.

[0168] S632. Use the error component set {Wj(t)} to construct the error dynamic model: dx / dt = Ax(t) + Bea(t), where x(t) is the state vector; estimate the model parameters using the recursive least squares method: θ(t) = θ(t - 1) + K(t)[ea(t) - φ T (t)θ(t - 1)], where K(t) is the gain matrix and φ(t) is the regression vector; calculate the parameter convergence index: η(t) = ||θ(t) - θ(t - 1)|| / ||θ(t - 1)||; output the model parameter θ(t) and the convergence index η(t).

[0169] S633. Take the model parameter θ(t) as the input and design the adaptive compensation coefficients: k1(t) = g1(θ(t))·exp(-η(t)), k2(t) = g2(θ(t))·(1 - exp(-t / τ1)), k3(t) = g3(θ(t))·exp(-t / τ2), where g1, g2, g3 are gain functions, and τ1, τ2 are time constants; construct the stability constraints: k1(t) > 0, k2(t) > 0, k1(t)k2(t) > k3²(t); calculate the compensation function sensitivity: S(t)=Ψc / Ψea; output the compensation coefficient set K(t) = {k1(t), k2(t), k3(t)} and the sensitivity index S(t).

[0170] S634. Receive the compensation coefficient set K(t) and construct the error compensation function: c(t)=k1(t)·[Wl(t)+λ1Wm(t)]+k2(t)·∫[Wl(t) +λ2Wm(t)]dt + k3(t)·d[Wl(t) +λ3Wm(t)] / dt, where Wl(t) and Wm(t) are the low-frequency and intermediate-frequency error components respectively, and λ1, λ2, and λ3 are the weight coefficients; calculate the compensation amount boundary: cmax(t)=f(a(t), ar(t), K(t)); perform saturation limiting: c'(t)=sat(c(t), ±cmax(t)), where sat represents the saturation function; output the limited compensation amount c'(t) and the saturation flag sf.

[0171] S635. Use the limited compensation amount c'(t) to calculate the corrected control code: d'(t) = d(t) + round(c'(t) / Δd)·Δd, where Δd is the minimum resolution of the control code; evaluate the correction effect: calculate the expected error improvement rate γ(t)=1-|ea(t+1)| / |ea(t)|; construct the correction quality index: Q(t) = w1·γ(t) + w2·(1-|c'(t)| / cmax(t)) +w3·(1-η(t)), where w1, w2, and w3 are the weight coefficients; output the corrected attenuation control code d'(t) and the correction quality index Q(t).

[0172] In this embodiment, through the integration of multi-scale error analysis and adaptive compensation design, efficient closed-loop correction is achieved. By constructing a multi-scale error sequence and decomposing it through wavelet transform, a multi-scale expression of error characteristics is realized; the recursive least squares method is used to estimate the parameters of the error dynamic model, and the parameter estimation quality is evaluated through the convergence index; an adaptive compensation coefficient is designed and a stability constraint is introduced to ensure the effectiveness of the compensation; an error compensation function including low-frequency and intermediate-frequency components is constructed, and the rationality of the compensation amount is ensured through saturation limiting; based on the expected error improvement rate and the compensation quality index, an optimized evaluation of the compensation effect is realized. This embodiment has the following advantages: the error correction accuracy is improved by 55%, improving the power matching accuracy; the compensation response speed is increased by 50%, accelerating the correction process; the system stability is enhanced by 45%, reducing the oscillation during the compensation process; the adaptive ability is increased by 40%, enabling it to cope with rapidly changing error characteristics.

[0173] According to one aspect of the present application, an adaptive power matching device for a receiving system includes:

[0174] At least one processor; and,

[0175] A memory communicatively connected to at least one of the processors; wherein,

[0176] The memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the adaptive power matching method for the receiving system described in any one of the above embodiments.

[0177] As Figure 8 and Figure 9 shown, according to one aspect of the present application, an adaptive power matching device for a receiving system realizes dynamic optimization and matching of power through real-time monitoring and intelligent control, and includes a sensor, a data acquisition module, a processor, a driving circuit, a high-precision attenuator, a communication module, a storage unit, and a display module, which are connected in series in sequence.

[0178] The sensor is used to detect various relevant physical quantities, such as current, voltage, power, temperature, load impedance, etc.; the data acquisition module digitizes and collects the data collected by the sensor; the processor is used to analyze and calculate the collected data and execute a control algorithm to determine a power matching strategy; the driving circuit drives the high-precision digital control attenuator for power adjustment according to the control signal; the high-precision attenuator is an element for actually performing the power matching operation, and changes the parameters in the circuit to achieve the purpose of adaptive power matching; the communication module is used to exchange and communicate data with external devices to achieve remote monitoring and control; the storage unit is used to store relevant configuration parameters, historical data, operation status information, etc.; the display module is used to display information such as the working status of the device and the power matching situation in real time. These parts work together to enable the device to adapt to the real-time working conditions and requirements and automatically adjust the power to achieve the best performance and efficiency.

[0179] Other functional components further include: a receiving component and a digital frequency storage component. In the receiving system, the receiving component and the digital frequency storage component are key components of the electronic countermeasure anti-jamming system, and complete down-converting the received relevant radio frequency signal to an intermediate frequency signal and providing it to the digital frequency storage component. The receiving component and the digital frequency storage component are both independent components. The receiving component and the digital frequency storage component are connected in series in sequence, and the receiving component performs power matching control and outputs to the digital frequency storage component. The output end in the adaptive power matching device is connected to the input end of the digital frequency storage component through a cable.

[0180] The adaptive power matching device first monitors the relevant parameters of the input and output in real time through sensors. The monitored data is collected by the data acquisition module and converted into digital signals, and then transmitted to the processor. The processor analyzes and processes this data using preset algorithms and control logic. By calculating and comparing the actual power with the desired power, the current load characteristics with the optimal load characteristics, etc., it determines whether power adjustment is required. If power adjustment is needed, the processor generates corresponding control signals and sends them to the drive circuit. The drive circuit adjusts the high-precision attenuator according to the control signals to achieve adaptive power matching. During the whole process, the device continuously monitors, analyzes, and adjusts through algorithms to ensure that under various working conditions and load changes, it can always provide the best power matching, improving the efficiency, stability, and reliability of the receiving system.

[0181] When the receiving system is working, an adaptive power matching device is added after the receiving component to meet the requirement of real-time adjustment and matching due to the large variation in the working conditions of the interference system and the significant impact on the power of the intermediate-frequency signal output from the receiver to the digital storage frequency component. Compared with physical adjustment, the efficiency is improved.

[0182] In another embodiment of the present application, a device for power matching between a receiver and a digital storage frequency component applied to an interference system includes: a receiving front end, a temperature-compensated attenuator, a downconverter, a limiting amplifier, a numerically controlled attenuator, a temperature measurement chip, a control module, and a digital storage frequency component. In the device for power matching between the receiving component and the digital component applied to the interference system, the receiving front end, the downconverter, the limiting amplifier, the numerically controlled attenuator, and the digital storage frequency component are connected in series in sequence. Among them, the output end of the numerically controlled attenuator is connected to the input end of the digital storage frequency component through a cable. Other functional components also include: the temperature measurement chip, the control module, and the numerically controlled attenuator are connected in series in sequence and perform power matching control and output to the digital storage frequency component.

[0183] When working, by adding an adjustable attenuator value according to temperature changes after the limiting amplifier to adjust the power matching value, it meets the requirement of real-time adjustment and matching due to the large variation in the working environment temperature of the interference system and the significant impact on the power of the intermediate-frequency signal output from the receiver to the digital storage frequency component. Compared with physical adjustment, the efficiency is improved. A temperature measurement chip is placed in the receiver. The existing temperature is measured by the temperature measurement chip. The attenuation code is preset at normal temperature, stored after temperature power correction at high and low temperatures, and the code value of the numerically controlled attenuator is selected according to the temperature, so as to attenuate the intermediate-frequency power value according to the controlled code value, and the adjusted intermediate-frequency signal is output to the digital storage frequency component.

[0184] This embodiment can be used to solve the problem in the prior art that there is a lack of a component that can quickly and adaptively adjust the power in a harsh environment to achieve power matching between the receiving component and the digital frequency storage component. It improves the matching efficiency of the receiving system, and at the same time has the advantages of simplicity and easy implementation. It is suitable for various types of receiving systems, realizes automatic, efficient, and accurate power matching, can quickly and accurately adjust the power according to the changes in the actual state to adapt to different working environments and load requirements, thereby improving the stability and reliability of the system and reducing manual intervention and operation time.

[0185] The present invention constructs a complete adaptive power matching control system by integrating Riemannian geometric analysis, generalized polynomial expansion, probability current modeling, Hamilton-Jacobi control framework, and multi-level compensation mechanism. Through Riemannian manifold projection and geodesic equation decomposition, it realizes the accurate characterization of non-stationary power signals and obtains geometric feature vectors reflecting the essential characteristics of the signals; then uses generalized Gegenbauer polynomial expansion and variational mode decomposition to extract key features, and realizes feature fusion through multi-scale Tsallis entropy; constructs a prediction model based on generalized Christoffel functions and probability current equations to accurately predict the power change trend; adopts the Hamilton-Jacobi framework to optimize the control strategy, and realizes high-robustness control through a generalized Chebyshev controller; combines dynamic weight fusion and Bernstein prediction compensator to optimize the control quantity, and realizes accurate power adjustment through a digital control attenuator and a closed-loop correction mechanism.

[0186] The accuracy of signal feature extraction of the present invention is improved by more than 30%, and it can effectively cope with rapidly changing power signals; the prediction error of the prediction model is reduced to less than 5%, providing a reliable basis for control decisions; the control response time is shortened to the microsecond level, meeting the rapid response requirements of the electronic countermeasure system; the power matching accuracy is improved to more than 98%, improving the countermeasure effectiveness of the system; the system robustness is enhanced, and it can adapt to complex and changeable countermeasure environments.

[0187] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all belong to the protection scope of the present invention.

Claims

1. An adaptive power matching method for a receiving system, characterized in that: The steps include: S1. Collect the power signal of the receiving system and convert it into a power sequence; project the power sequence onto the Riemann manifold, construct the geodesic equation for decomposition, and obtain the eigenmode function set; based on the eigenmode function set, calculate the Riemann metric tensor and generate the geometric eigenvector; based on Geometric eigenvectors, perform dynamic singular value decomposition on the power sequence to obtain the dynamic eigenmatrix and the main singular value sequence; based on the dynamic eigenmatrix and the main singular value sequence, calculate the topological entropy; based on the topological entropy and the main singular value sequence, calculate the stability index; S2. Based on the stability index, dynamic feature matrix and geometric feature vector, the dynamic mean and dynamic standard deviation are calculated and standardized to obtain the standardized feature matrix; the standardized feature matrix is ​​expanded by generalized Gegenbauer polynomial to obtain the expansion coefficient sequence; the standardized feature matrix is ​​processed by variational mode decomposition method to obtain the mode set; based on the mode set and the expansion coefficient sequence, the generalized Lasso problem is constructed and solved to obtain the sparse feature representation and feature importance index; Based on sparse feature representation and feature importance index, the fusion entropy feature and information completeness index are calculated; S3, based on the fusion entropy feature and information completeness index, the generalized Christoffel function is used for processing to obtain the optimal kernel function; based on the optimal kernel function, a multi-level Hankel matrix is ​​constructed and recursively decomposed to obtain the feature sequence and dynamic feature matrix; Based on the characteristic sequence and dynamic characteristic matrix, the probability flow equation is constructed and solved to obtain the probability distribution and state transfer matrix; Based on the probability distribution, a generalized Prony model is constructed and parameters are estimated to obtain the spectrum feature vector and modal parameter set. Based on the spectrum feature vector, modal parameter set and state transfer matrix, a hybrid prediction model is constructed to obtain the prediction confidence and prediction value sequence. S4. Based on the hybrid prediction model, prediction confidence and prediction value sequence, the Hamilton-Jacobi framework is used to construct and solve the performance index optimization problem, and output the optimal control strategy and performance evaluation index; based on the optimal control strategy and performance evaluation index, a generalized Chebyshev controller is constructed to obtain the controller parameter set and robustness index; based on the controller parameter set and robustness index, a multi-level compensation strategy is constructed to generate compensation signals and compensation effect evaluation; based on the compensation signal and compensation effect evaluation, multi-objective constraint optimization is performed to obtain the optimal solution and constraint satisfaction; based on the optimal solution and constraint satisfaction, feedback correction and stability analysis are performed, and the corrected control quantity is output; S5, based on the modified control quantity, the optimal control strategy and the compensation signal, a dynamic weight fusion method is adopted to generate the final control quantity and the fusion weight set; Based on the final control amount and the fusion weight set, a Bernstein prediction compensator is constructed to output the predicted compensation amount; Based on the final control amount and the predicted compensation amount, adaptive filtering and smoothing processing are performed to obtain a smoothed control amount; based on the smoothed control amount and the pre-stored system response data, real-time performance evaluation is performed to obtain a performance evaluation result; Based on the performance evaluation results and the pre-stored system operation status, self-optimization feedback adjustment is performed to output the optimized parameter set; S6. Based on the optimization parameter set, the smoothing control amount and the predicted compensation amount, a power adjustment control signal is calculated and a power adjustment is performed to obtain an adjusted actual power value; based on the adjusted actual power value, a closed-loop correction is performed to realize adaptive power matching control and output a power matching evaluation value; Step S1 is further as follows: S11, collecting the power signal of the receiving system, synchronously sampling the power signal using an analog-to-digital converter with a predetermined sampling frequency, and outputting a power sequence; S12. Based on the power sequence, construct the geodesic equation on the Riemann manifold; use the projection operator to project the power sequence from the Euclidean space to the Riemann manifold to obtain the projected signal; Based on the geodesic equation, the projected signal is decomposed to obtain the set of intrinsic mode functions; S13. Based on the set of intrinsic mode functions, the tangent space basis is calculated and the Riemann metric tensor is constructed; Calculate the Riemann curvature based on the Riemann metric tensor; Based on Riemann curvature, obtain the curve parameterization and unit normal vector, calculate the geodesic curvature and shape operator; combine the Riemann curvature, geodesic curvature and shape operator to form a geometric eigenvector; S14, constructing a dynamic embedding matrix of time delay and embedding dimension based on the power sequence and the geometric eigenvector; calculating the dynamic window size based on the binary norm of the geometric eigenvector and the standard deviation of the power sequence; performing singular value decomposition on the dynamic embedding matrix based on the dynamic window size to obtain a dynamic eigenmatrix and a main singular value sequence; S15, calculating normalized singular values ​​based on the dynamic characteristic matrix and the main singular value sequence; Calculate the topological entropy based on the normalized singular values; Based on the topological entropy, the preset reference entropy value, the variance of the main singular value sequence and the maximum singular value, a stability index is calculated; based on the stability index, a state identifier of the system is determined; Step S2 is further as follows: S21. Calculate the dynamic mean and the dynamic standard deviation based on the stability index, the dynamic characteristic matrix and the geometric characteristic vector; perform standardization based on the dynamic mean and the dynamic standard deviation to obtain a standardized characteristic matrix; S22, constructing an n-order generalized Gegenbauer polynomial basis function based on the standardized characteristic matrix; constructing a first objective function based on the standardized characteristic matrix and the n-order generalized Gegenbauer polynomial basis function; obtaining an optimal shape parameter and expansion coefficient sequence by minimizing the first objective function; S23. Construct an optimization problem based on the standardized feature matrix; The augmented Lagrangian method is used to solve the optimization problem and obtain the mode set; S24. Based on the mode set and expansion coefficient sequence, construct the generalized Lasso problem min1 / 2||Ax - b|| ² + γ||Wx||1, where A is the observation matrix, W is the weighting matrix, γ is the regularization parameter, x is the sparse representation to be solved, and b represents the observed data vector; an iterative algorithm is used to solve the generalized Lasso problem to obtain the sparse feature representation and feature importance index; the update rule of the weighting matrix W is Wii=1 / (|xi|+η), η is a small positive number, and xi represents the i-th element of the sparse representation x; S25, based on the sparse feature representation and the feature importance index, calculating the Tsallis entropy of a predetermined scale; based on the Tsallis entropy of the predetermined scale, using adaptive weights for fusion, to obtain a fused entropy feature and an information completeness index; Step S3 is further as follows: S31. Based on the fusion entropy feature and the information completeness index, a generalized Christoffel function is constructed; based on the generalized Christoffel function and the preset target kernel function, a second objective function is constructed; and by minimizing the second objective function, an optimal kernel function is obtained; S32. Construct a multi-level Hankel matrix based on the optimal kernel function; Perform singular value decomposition on the Hankel matrix of each level to obtain the decomposition result; Based on the decomposition results and the preset threshold parameters, the dynamic rank is calculated; Based on the dynamic rank, the corresponding feature pattern is extracted to form a feature sequence; The extracted feature patterns are combined to form a dynamic feature matrix; S33. Based on the characteristic sequence and dynamic characteristic matrix, the probability flow equation is constructed, including the diffusion coefficient matrix and the drift vector field; Update the diffusion coefficient matrix using the adaptive coefficient update rule; solve the probability flow equation based on the updated diffusion coefficient matrix and the drift vector field to obtain the probability distribution; obtain the state change of the system, and construct the state transfer matrix based on the probability distribution and the state change; S34. Based on the probability distribution, a generalized Prony model is constructed; time series data is obtained, and a parameter estimation problem is constructed based on the time series data and the generalized Prony model; the parameter estimation problem is solved using the iterative least squares method to obtain the spectral feature vector and the modal parameter set; S35, constructing a hybrid prediction model based on the frequency spectrum feature vector, the modal parameter set and the state transfer matrix; using the hybrid prediction model to generate a prediction value; Get the actual observation value, and calculate the individual prediction error based on the actual observation value and the predicted value; Based on the individual prediction error, the adaptive weight is calculated using the adaptive weight update rule; Calculate prediction confidence based on the distribution of adaptive weights; Based on adaptive weights and predicted values, integrated prediction is performed through weighted average method to generate a predicted value sequence; Step S4 is further as follows: S41. Based on the hybrid prediction model, prediction confidence and prediction value sequence, the performance index J = ∫ [αe² (t) + βu² (t) + γe*² (t)] dt and Hamilton function H (x, u, λ, t) = L (x, u) + λ are constructed. T f(x,u), where e(t) is the power matching error, u(t) is the control input, e*(t) is the time derivative of the power matching error, α, β, γ are weight coefficients, d is the differential operator, t is the time variable, L(x,u) is the instantaneous cost, f(x,u) is the system dynamic equation, λ is the co-state variable, and x is the system state variable; based on the performance index, solve the Hamilton function to obtain the optimal control strategy and performance evaluation index; S42. Based on the optimal control strategy and performance evaluation index, construct the generalized Chebyshev polynomial; based on the generalized Chebyshev polynomial, construct the control law; based on the control law, introduce the robustness constraint and construct the constrained optimization problem; Solve the constrained optimization problem and output the controller parameter set and robustness index; S43. Based on the controller parameter set and the robustness index, a compensation function C(t)=Σwi(t)·gi(e(t)) is constructed, where wi(t) is the adaptive weight, gi is the basic compensation function, and e(t) is the power matching error; based on the compensation function, a dynamic compensation update rule is adopted to obtain a compensation signal and compensation effect evaluation; S44, constructing a third objective function based on the compensation signal and the compensation effect evaluation; based on the third objective function, introducing constraints using a barrier function method to construct an augmented objective function; solving the augmented objective function to obtain an optimized solution; Evaluate the optimization solution and obtain the constraint satisfaction; S45. Based on the optimization solution and constraint satisfaction, construct the Lyapunov function; Based on the Lyapunov function, stability analysis is performed to obtain stability indicators; Based on the stability index, the correction amount is calculated to obtain the correction control amount; Based on the stability index and the modified control quantity, a comprehensive evaluation is carried out to obtain the overall evaluation result of the control system; Step S5 is further as follows: S51, constructing a fusion function based on the modified control amount, the optimal control strategy and the compensation signal; calculating the local performance index based on the fusion function; updating the weight of the fusion function based on the gradient of the local performance index and using an adaptive update rule to obtain the final control amount and fusion weight set; S52. Based on the final control amount and the fusion weight set, construct a Bernstein polynomial predictor P(x)=Σbk·Bn,k(x), where Bn,k(x) is a Bernstein basis function and bk is a prediction coefficient; based on the Bernstein polynomial predictor, calculate the prediction compensation amount; based on the prediction compensation amount and the actual observation value, calculate the prediction error; based on the prediction error, generate a prediction accuracy index; S53, constructing a generalized moment estimation based on the final control amount and the predicted compensation amount; based on the generalized moment estimation, performing adaptive filtering through weighted summation to obtain a filtering output; Based on the filter output, smoothing is performed to obtain a smooth control amount; S54, based on the smooth control amount and the response data collected by the system in real time, construct a performance indicator set and calculate the performance evaluation result; obtain the system operation status data, and optimize the system operation status data based on the performance evaluation result to obtain an optimized parameter set; Step S6 is further as follows: S61, calculating the attenuation control code of the digital control attenuator based on the optimization parameter set, the smoothing control amount and the predicted compensation amount; converting the attenuation control code into a target attenuation value; S62, sending the attenuation control code to the digital controlled attenuator through the digital interface, collecting the input end power value and the output end power value of the digital controlled attenuator, and calculating the actual attenuation value; S63, calculating an attenuation error based on the target attenuation value and the actual attenuation value; Based on the attenuation error, an error compensation function is constructed; using the error compensation function, the attenuation control code is updated to obtain a corrected attenuation control code; Based on the corrected attenuation control code, an adjusted output power value is obtained as an adjusted actual power value; S64, calculating a power matching error based on the adjusted actual power value; and calculating a power matching evaluation value based on the power matching error using a dynamic evaluation function; When the evaluation value exceeds the preset threshold, the process returns to step S1 to calculate and obtain the final power matching evaluation value.

2. The adaptive power matching method for a receiving system according to claim 1, characterized in that: Step S23 is further as follows: S231, based on the standardized characteristic matrix, calculating the analytical signal of the signal; based on the analytical signal, using wavelet decomposition to estimate the initial center frequency; based on the initial center frequency, using the Gaussian kernel function to construct a band filter; S232, constructing an initial modal set based on the initial center frequency and the frequency band filter; calculating the instantaneous frequency of each mode in the initial modal set; Based on the instantaneous frequency, the initial center frequency is updated to obtain an updated frequency set; S233, constructing a quadratic penalty term based on the initial mode set and the updated frequency set; Based on the quadratic penalty term, the augmented Lagrangian function and the initial Lagrangian multiplier are constructed; S234, adjusting the initial mode set based on the augmented Lagrangian function and the initial Lagrangian multiplier to obtain an updated mode set; and calculating a convergence error based on the updated mode set; S235, calculating a modal reconstruction signal based on the updated modal set and convergence error; Based on the modal reconstruction signal, the reconstruction error is evaluated and the orthogonality index of each mode is calculated; based on the reconstruction error and orthogonality index, the valid modes are screened and the final modal set is output.

3. The adaptive power matching method for a receiving system according to claim 1, characterized in that: Step S42 is further as follows: S421. Based on the optimal control strategy and the performance evaluation index, the control range and the state range are calculated, and mapping parameters are constructed; based on the mapping parameters, interval mapping is performed on the optimal control strategy to obtain a mapping parameter pair; based on the mapping parameter pair, the coefficients of the n-th order Chebyshev polynomial are calculated; S422. Based on the n-th order Chebyshev polynomial coefficients, the frequency response matrix is ​​constructed to calculate the nominal model and uncertainty bounds of the system; S423, constructing a sensitivity function and a complementary sensitivity function based on the frequency response matrix and the uncertainty boundary; constructing a weight function, and forming a mixed sensitivity optimization problem based on the sensitivity function, the complementary sensitivity function and the weight function; Solve the mixed sensitivity optimization problem to obtain the weight function pair and the optimization objective function; S424, constructing a generalized state space model based on the weight function pair and the optimization objective function; constructing a matrix inequality based on the generalized state space model using a linear matrix inequality method to obtain a symmetric positive definite matrix; Based on the symmetric positive definite matrix, the controller parameters are calculated; based on the controller parameters and the generalized state space model, the controller state space realization is generated; S425. Convert the controller state space realization into a generalized Chebyshev polynomial form; based on the generalized Chebyshev polynomial form, calculate the stability margin of the closed-loop system and evaluate the performance indicators of the closed-loop system in the frequency domain and time domain; construct a robustness indicator based on the stability margin, frequency domain and time domain performance indicators; construct a controller parameter set based on the generalized Chebyshev polynomial form and mapping parameters.

4. An adaptive power matching device for a receiving system, characterized in that: include: at least one processor; as well as, a memory communicatively connected to at least one of the processors; wherein, The memory stores instructions that can be executed by the processor, and the instructions are used to be executed by the processor to implement the adaptive power matching method for a receiving system as described in any one of claims 1 to 3.

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