Design Method and System of a Networked Two-Dimensional System Anti-Outlier Proportional-Integral Observer

Abstract

The present invention discloses a design method and system for a networked two-dimensional system anti-outlier proportional-integral observer, including: establishing a state space model of a networked two-dimensional discrete system, and preliminarily modeling the state vector of the system, the process noise existing in the system, and the non-linear terms; constructing a redundant channel measurement output with bidirectional evolution characteristics; designing an anti-outlier proportional-integral observer structure with an adaptive saturation function, and giving the parameters of the designed observer gain matrix; defining the estimated value and the estimation error of the state vector of the system, defining an augmented vector, and transforming the networked two-dimensional discrete system into an augmented dynamic estimation error system; introducing a system performance evaluation index, substituting the parameters of the observer gain matrix into the augmented dynamic estimation error system, and if the performance index constraints are satisfied, ending the system design; the present invention reduces the influence of non-linear factors, bounded disturbances, and measurement outliers, and effectively improves the reliability and safety of the networked two-dimensional system.

Description

Technical Field

[0001] The present invention relates to the technical field of networked systems, and more specifically, to a design method and system for a networked two-dimensional system anti-outlier proportional integral observer. Background Art

[0002] In recent years, two-dimensional systems have attracted the attention of scholars because they can be widely applied to various multivariable systems, including multivariable network implementation, seismic exploration data processing, transmission lines, X-ray image enhancement and other systems. Therefore, two-dimensional system theory has become one of the most promising fields in control science.

[0003] On the other hand, control theory has developed from classical point-to-point control to distributed and networked. Networked control systems have emerged under this background; a networked control system is a closed-loop feedback control system formed by the highly integrated interaction of network units and controlled objects through a shared network. Because of its advantages such as low cost, simple installation, and convenient maintenance, it has received continuous attention from domestic and foreign scholars in recent years and has been widely applied in many practical engineering fields.

[0004] However, in practical applications, the introduction of a communication shared network increases the flexibility and expandability of the system, while some adverse factors of network-induced problems caused by network characteristics, such as packet loss, transmission delay, quantization error, network attack and measurement outliers, will lead to the deterioration of the system performance and even affect the stability of the system; on the other hand, due to the gradual increase in the scale and complexity of modern industrial systems and the limitations of the internal structure of the system, it is often difficult to directly obtain the internal state of the system, which results in that the control method based on the system state cannot be directly applied to the controlled system in practical applications.

[0005] Therefore, how to comprehensively consider various non-ideal network factors when studying networked systems and use the measurable information to ensure the filter performance to the greatest extent under the influence of network-induced problems is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a design method and system for a networked two-dimensional system anti-outlier proportional integral observer to solve some of the technical problems mentioned in the background art.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A design method for a networked two-dimensional system anti-outlier proportional integral observer based on a redundant channel protocol, comprising the following steps:

[0009] S1. Establish a state - space model of a networked two - dimensional discrete system with non - linear factors and external disturbances, and preliminarily model the state vector of the system, the process noise existing in the system, and the non - linear terms.

[0010] S2. Construct a redundant - channel measurement output with two - way evolution characteristics. When packet loss occurs in the main channel, the backup channel takes over the transmission of the measurement data signal of the main channel.

[0011] S3. Design an anti - outlier proportional - integral observer structure with an adaptive saturation function, and give the parameters of the designed observer gain matrix.

[0012] S4. Define the estimated value and the estimation error of the state vector of the system, define the augmented vector, and comprehensively consider the influence of measurement outliers and the redundant - channel mechanism on the networked two - dimensional system. Convert the networked two - dimensional discrete system in step S1 into an augmented dynamic estimation error system.

[0013] S5. Introduce a system performance evaluation index, substitute the parameters of the designed observer gain matrix into the augmented dynamic estimation error system in step S4, and judge whether the augmented dynamic estimation error system satisfies finite - time boundedness in the mean - square sense. If the performance index constraints are met, end the system design and obtain the final anti - outlier proportional - integral observer structure; otherwise, repeat steps S3 to S5.

[0014] S6. Use the obtained final anti - outlier proportional - integral observer structure to perform state tracking on the networked two - dimensional discrete system.

[0015] Preferably, the state - space model of the networked two - dimensional discrete system in step S1 is:

[0016] x (i+1,j+1) =A 1，(i+1,j) x (i+1,j) +A 2，(i，j+1) x (i，j+1) +F 1，(i+1,j) f(x i+1,j) )+F 2，(i，j+1) f(x (i，j+1) )+B 1，(i+1，j) ω (i+1，j) +B 2，(i，j+1) ω (i，j+1 )

[0017] Where, is the state vector of the networked two - dimensional system, is the process noise with zero mean and variance W of the networked two - dimensional system, n x is the dimension of the system state vector, n ω is the dimension of the input vector, and is a time-varying system matrix of known dimension, and f(x (i，j) ) is the smooth non-linear factor existing in the networked two-dimensional system.

[0018] Preferably, the redundant channel measurement output with two-way evolution characteristics constructed in step S2 is specifically:

[0019]

[0020] Among them, r ∈ {1, 2,..., N}, and y r(i，j) is the output of the r-th measurement channel at time (i, j), and N is the number of redundant channels in the networked two-dimensional system. and are known time-varying matrices;

[0021] According to the uncertainty and discontinuity of the occurrence of packet loss phenomena, a random variable σ r，(i，j) subject to a Bernoulli distribution is defined to represent whether packet loss occurs in the r-th channel at time (i, j), taking values of 0 or 1, where 0 represents the occurrence of packet loss in the channel, and 1 represents that no packet loss occurs in the channel:

[0022]

[0023]

[0024] The redundant channel measurement output is reconstructed as:

[0025] y (i，j) = Φ (i,j) C (i,j) x (i，j) + D (i，j) ω (i,j) ;

[0026] Among them,

[0027]

[0028] If the random variable σ 1，(i，j) = 1, then no packet loss occurs on the main channel, and the redundant channel will not be activated; if the random variable σ m，(i，j) = 1 and σ r(i，j) = 0, m ∈ [2, N], r ∈ [1, m - 1], then packet loss occurs in the (r - 1)-th channel, and normal data packets will be transmitted through the r-th channel.

[0029] Preferably, the structure of the anti-outlier proportional-integral observer with an adaptive saturation function designed in step S3 is specifically:

[0030]

[0031] Among them, is the estimated value of the system state vector x (i，j) , is the measurement output y (i，j) and its estimate is the weighted error value between them, and are the parameters of the designed proportional-integral observer gain matrix, is the non-linear saturation function.

[0032] Preferably, for step S4:

[0033] Define the error between the state vector x of the networked two-dimensional system (i,j) and its estimated value as The weighted error is χ (i，j) , let n = 2n x + n δ , construct the augmented matrix:

[0034]

[0035] Then, the augmented dynamic estimation error system is specifically:

[0036]

[0037] Among them,

[0038]

[0039]

[0040] m ∈ [2, N].

[0041] Preferably, step S5 also includes using the Lyapunov stability theory and linear matrix inequality analysis method to obtain the sufficient conditions for the augmented dynamic estimation error system to satisfy finite-time boundedness in the mean-square sense and the existence of the proportional-integral observer, and solving the observer gain matrix.

[0042] Preferably, the system performance evaluation index introduced in step S5 is:

[0043] If there exists a finite-time domain function and the augmented dynamic estimation error system η ( i, j ) satisfies the following constraints:

[0044]

[0045] Then the augmented dynamic estimation error system η( i, j ) is considered to be bounded in the finite time domain in the sense of mean square, where E{·} represents taking the mean value of a certain variable, and π 0 represents a preset upper bound;

[0046] A sufficient condition for the augmented dynamic estimation error system to be bounded in the finite time domain in the sense of mean square is:

[0047]

[0048] Solve. If there exists a positive definite symmetric matrix P (i+1,j+1) , R (i+1,j+1) , P (i+1,j) , R (i,j+1) , Q 1,(i+1,j) and Q 2,(i,j+1) , and matrices of appropriate dimensions and such that the inequality of the sufficient condition holds, then the system is bounded in the finite time domain in the sense of mean square under the influence of measurement outliers and the redundant channel protocol, and the system estimation value can track the system state;

[0049] The specific proportional-integral observer gain matrix obtained by solving is:

[0050]

[0051] A system for designing an outlier-resistant proportional-integral observer for a networked two-dimensional system based on a redundant channel protocol, based on the above-mentioned method for designing an outlier-resistant proportional-integral observer for a networked two-dimensional system based on a redundant channel protocol, includes a state space model construction module for a networked two-dimensional discrete system, a redundant channel measurement output module, an outlier-resistant proportional-integral observer structure design module, an augmented dynamic estimation error system establishment module, an observer gain solution module, and a state tracking module;

[0052] The state space model construction module for a networked two-dimensional discrete system is used to establish a state space model for a networked two-dimensional discrete system with nonlinear factors and external disturbances, and to preliminarily model the state vector of the system, the process noise existing in the system, and the nonlinear terms;

[0053] The redundant channel measurement output module is used to construct a redundant channel measurement output with two-way evolution characteristics, and when a data packet loss phenomenon occurs in the main channel, the backup channel takes over the main channel to transmit the measurement data signal;

[0054] The outlier-resistant proportional-integral observer structure design module is used to design an outlier-resistant proportional-integral observer structure with an adaptive saturation function and to give the parameter of the designed observer gain matrix;

[0055] An augmented dynamic estimation error system establishment module, which is used to define the estimated value and estimation error of the state vector of the system, define the augmented vector, comprehensively consider the influence of measurement outliers and redundant channel mechanisms on the networked two-dimensional system, and transform the networked two-dimensional discrete system into an augmented dynamic estimation error system;

[0056] An observer gain solution module, which is used to introduce system performance evaluation indicators, substitute the designed observer gain matrix parameters into the augmented dynamic estimation error system, determine whether the augmented dynamic estimation error system meets the performance index constraints of being bounded in the finite time domain in the mean square sense, solve the proportional-integral observer gain matrix, and obtain the final outlier-resistant proportional-integral observer structure;

[0057] A state tracking module, which is used to perform state tracking on the networked two-dimensional discrete system by using the obtained final outlier-resistant proportional-integral observer structure.

[0058] A computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the described method for designing an outlier-resistant proportional-integral observer for a networked two-dimensional system based on a redundant channel protocol.

[0059] A processing terminal, including a memory and a processor. A computer program that can run on the processor is stored in the memory. When the processor executes the computer program, it implements the described method for designing an outlier-resistant proportional-integral observer for a networked two-dimensional system based on a redundant channel protocol.

[0060] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method and system for designing an outlier-resistant proportional-integral observer for a networked two-dimensional system. For a discrete-time networked two-dimensional system under a redundant channel protocol, an outlier-resistant proportional-integral observer design strategy is proposed, integrating advanced technologies including an augmentation method, an adaptive saturation function, an optimization algorithm, and a redundant channel protocol to design an observer, which can better estimate the state of the system and successfully suppress the influence of measurement outliers on the system, effectively improving the reliability and security of the networked two-dimensional system, and helping to reduce the influence of nonlinear factors, bounded disturbances, and measurement outliers commonly existing in the actual industrial field of the system. Description of the Drawings

[0061] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0062] Figure 1The accompanying drawing is a schematic diagram of the design method of a networked two-dimensional system anti-outlier proportional-integral observer based on a redundant channel protocol provided by the present invention;

[0063] Figure 2 The accompanying drawing is a comparison schematic diagram of the first component x of the state of the networked two-dimensional system provided by the present invention 1，(i，j) and its estimated value;

[0064] Figure 3 The accompanying drawing is a comparison schematic diagram of the second component x of the state of the networked two-dimensional system provided by the present invention 2，(i，j) and its estimated value;

[0065] Figure 4 The accompanying drawing is a schematic diagram of the state of the dynamic estimation error system provided by the present invention;

[0066] Figure 5 The accompanying drawing is a schematic diagram of the evolution of the adaptive saturation threshold trajectory provided by the present invention;

[0067] Figure 6 The accompanying drawing is a comparison schematic diagram of the first component of the estimated value of the anti-outlier proportional-integral observer and the estimated value of the traditional proportional-integral observer provided by the present invention;

[0068] Figure 7 The accompanying drawing is a schematic diagram of the second component of the estimated value of the anti-outlier proportional-integral observer and the estimated value of the traditional proportional-integral observer provided by the present invention. Specific embodiments

[0069] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0070] The embodiments of the present invention disclose a design method of an anti-outlier proportional-integral observer for a networked two-dimensional system based on a redundant channel protocol, as Figure 1 , including the following steps:

[0071] S1. Establish a state space model of a networked two-dimensional discrete system with nonlinear factors and external disturbances, and perform preliminary modeling on the state vector Process noise existing in the system and the nonlinear term ;

[0072] S2. Construct a redundant channel measurement output with bidirectional evolution characteristics When packet loss occurs in the main channel, the backup channel takes over the transmission of measurement data signals in the main channel to improve the reliability of the networked two-dimensional system;

[0073] S3. Design an anti-outlier proportional-integral observer structure with an adaptive saturation function, and give the parameters of the designed observer gain matrix;

[0074] S4. Define the estimated value of the state vector of the system and the estimation error Define the augmented vector and Considering the influence of measurement outliers and redundant channel mechanism on the networked two-dimensional system, transform the networked two-dimensional discrete system in step S1 into an augmented dynamic estimation error system;

[0075] S5. Introduce the system performance evaluation index, substitute the parameters of the designed observer gain matrix into the augmented dynamic estimation error system in step S4, and judge whether the augmented dynamic estimation error system satisfies finite-time boundedness in the mean square sense. If the performance index constraints are satisfied, end the system design and obtain the final anti-outlier proportional-integral observer structure; otherwise, repeat steps S3 to S5;

[0076] S6. Use the obtained final anti-outlier proportional-integral observer structure to perform state tracking on the networked two-dimensional discrete system.

[0077] To further implement the above technical solution, the state space model of the networked two-dimensional discrete system in step S1 is:

[0078] x (i+1,j+1) =A 1，(i+1，j) x (i+1,j) +A 2，(i,j+1) x (i,j+1) +F 1，(i+1,j) f(x (i+1,j) )+F 2(i，j+1) f(x (i，j+1) )+B 1,(i+1，j) ω (i+1，j) +B 2，(i，j+1) ω (i，j+1)

[0079] where, is the state vector of the networked two-dimensional system, is the process noise with zero mean and variance W for the networked two-dimensional system, n x is the dimension of the system state vector, n ω is the dimension of the input vector, and are time-varying system matrices with known dimensions, f(x (i，j)) is the smooth non - linear factor existing in the networked two - dimensional system.

[0080] In this embodiment, the non - linear function is defined as:

[0081] f(0) = 0

[0082]

[0083] where, G 1，(i，j) and G 2(i，j) are known constant matrices with appropriate dimensions.

[0084] To further implement the above - mentioned technical solution, a redundant channel protocol is introduced to reduce the probability of packet loss and thus improve the reliability of the communication network. Then, the redundant channel measurement output with two - way evolution characteristics constructed in step S2 is specifically:

[0085]

[0086] where, r ∈ {1, 2,..., N}, y r，(i，j) is the output of the r - th measurement channel at time (i, j), N is the number of redundant channels in the networked two - dimensional system, and are known time - varying matrices;

[0087] According to the uncertainty and discontinuity of the occurrence of packet loss phenomenon, a random variable σ r，(i，j) obeying the Bernoulli distribution is defined to represent whether packet loss occurs in the r - th channel at time (i, j). Its value is 0 or 1. 0 represents that packet loss occurs in the channel, and 1 represents that no packet loss occurs in the channel:

[0088]

[0089] is a known constant representing the probability of packet loss in the r - th channel;

[0090] The redundant channel measurement output is reconstructed as:

[0091] y (i，j) = Φ (i，j) C (i，j) x (i，j) + D (i，j) ω (i，j) ;

[0092] where,

[0093]

[0094] If the random variable σ1，(i，j) If σ m，(i，j) = 1, no packet loss occurs on the primary channel, and the redundant channel will not be activated; if the random variable σ r，(i，j) = 1 and σ

[0095] In this embodiment, the setting and installation of the redundant channel reduce the probability of packet loss from to and improve the reliability of the communication network.

[0096] To further implement the above technical solution, the structure of the anti-outlier proportional-integral observer with an adaptive saturation function designed in step S3 is specifically:

[0097]

[0098] where is the estimated value of the system state vector x (i，j) , is the weighted error value between the measured output y (i，j) and its estimate , and are the designed proportional-integral observer gain matrix parameters, is the nonlinear saturation function.

[0099] In this embodiment, the nonlinear saturation function is specifically:

[0100]

[0101] where is the s-th vector in the saturation function, and the saturation threshold δ (i，j) is a positive scalar, which is adaptively adjusted according to the error between the measured output y (i，j) and its estimated value ;

[0102] δ (i，j) The specific evolution process is:

[0103]

[0104] where α 1 , α 2 ∈[0, 1 / 2) are weight coefficients, and are positive definite symmetric matrices with appropriate dimensions;

[0105] Adaptive saturation threshold δ (i，j) The evolution of depends on its own characteristics and the error between the measurement output and its estimated value. Specifically, based on the stability criterion of the two-dimensional system, the parameter α 1 and α 2 will cause the gradual convergence of δ (i，j) , while the appropriate weighting matrices R 1 and R 2 ensure the convergence smoothness of δ (i，j) ; if there are no measurement outliers, the adaptive saturation threshold δ (i，j) will decrease as the error between the measurement output y (i，j) and its estimated value gradually decreases; and if there are measurement outliers beyond the normal data, the adaptive saturation threshold will become larger at the moment of measurement outliers. By introducing an update mechanism for the adaptive saturation threshold with two-way evolution, the adaptive saturation threshold proportional-integral observer not only ensures the outlier resistance performance, but also has better estimation performance compared with the proportional-integral observer structure using a fixed threshold level.

[0106] To further implement the above technical solution, for step S4:

[0107] Define the error between the state vector x (i,j) of the networked two-dimensional system and its estimated value as The weighted error is χ (i，j) , let n = 2n x + n δ , and construct the augmented matrix:

[0108]

[0109] The dynamic evolution law of the estimation error e (i，j) is:

[0110]

[0111] Then, the augmented dynamic estimation error system is specifically:

[0112]

[0113] Among them,

[0114]

[0115]

[0116] m ∈ [2, N].

[0117] The newly constructed augmented dynamic estimation error system η (i，j)It is composed of the original system state vector x (i，j) , the estimation error e (i，j) and the weighted error χ (i，j) ; if the augmented dynamic estimation error system is bounded, then the estimation error is also bounded.

[0118] To further implement the above technical solution, step S5 further includes using the Lyapunov stability theory and the linear matrix inequality analysis method to obtain the sufficient conditions for the augmented dynamic estimation error system to satisfy boundedness in the mean square sense over a finite time domain and the existence of a proportional-integral observer, and solving the observer gain matrix. Specifically:

[0119] For the dynamic estimation error system η(i,j ) select a suitable Lyapunov function:

[0120]

[0121] where P ( i,j ) and R ( i,j ) are positive definite symmetric matrices, λ 1 and λ 2 are positive scalars;

[0122] Define the function

[0123] where,

[0124] Using the Lyapunov stability theory and the linear matrix inequality analysis method, obtain the sufficient conditions for boundedness, specifically:

[0125] Assume the following linear matrix inequality holds:

[0126]

[0127] where

[0128]

[0129] In addition, the parameters

[0130]

[0131] and are unknown matrices to be determined, and the parameters γ 1,(i+1,j) , γ 2,(i,j+1) , ρ, λ 1, λ 2 is a given positive scalar, and satisfies γ 1,(i+1,j) > 0, γ 2,(i,j+1) > 0, ρ > 1, λ 1 > 0, λ 2 > 0, * represents the transpose of a symmetric position matrix, and I represents the identity matrix with appropriate dimensions.

[0132] Taking the difference of the Lyapunov function along the trajectory of the dynamic estimation error system η (ij) yields:

[0133]

[0134] Considering that the nonlinear function f(·) satisfies the sector boundedness condition of Assumption 1 at times (i + 1, j) and (i, j + 1), we can obtain:

[0135]

[0136] Furthermore, considering the introduction of the saturation function on the dynamic estimation error system η (i,j) results in:

[0137]

[0138] It can be deduced that:

[0139]

[0140] where:

[0141]

[0142] If the matrix Ω < 0, it is easy to obtain:

[0143]

[0144] Furthermore, it can be calculated that:

[0145]

[0146] It can be iteratively obtained that:

[0147]

[0148] In addition, according to the Lyapunov function condition, it can be obtained that:

[0149]

[0150] This further shows that:

[0151]

[0152] To further implement the above technical solution, the system performance evaluation index introduced in step S5 is as follows:

[0153] If there exists a finite-time domain function and the augmented dynamic estimation error system η (i,j) satisfies the following constraints:

[0154]

[0155] then the augmented dynamic estimation error system η (i,j) is considered to be finite-time bounded in the mean-square sense, where E{·} represents taking the mean value of a certain variable, and π 0 represents a preset upper bound;

[0156] The sufficient condition for the augmented dynamic estimation error system to satisfy finite-time boundedness in the mean-square sense is:

[0157]

[0158] Solve. If there exist positive definite symmetric matrices P (i+1,j+1) , R (i+1,j+1) , P(i + 1, j), R (i,j+1) , Q 1,(i+1,j) and Q 2,(i,j+1) , and matrices of appropriate dimensions such that the inequality of the sufficient condition holds, then the system is finite-time bounded in the mean-square sense under the influence of measurement outliers and redundant channel protocols, and the system estimation value can track the system state;

[0159] The specific proportional-integral observer gain matrix obtained by solving is:

[0160]

[0161] The method for solving the observer gain is:

[0162] Define the matrix:

[0163]

[0164] By applying the Schur complement lemma to and multiplying the matrix Ω on the left and right by the diagonal matrices

[0165] and using the variable substitution:

[0166]

[0167] we can further obtain

[0168]

[0169] They are all unknown variables, and other variables are all known, which can be obtained according to the system parameters or directly given. The LMI toolbox in Matlab software is used for solution to obtain the observer parameter matrix that makes the dynamic estimation error system mean-square bounded.

[0170] In another embodiment, a discrete-time model is constructed by using several typical indexes in the industrial heat exchange process to verify the effectiveness of the designed anti-outlier proportional-integral observer. Specifically:

[0171] Consider the industrial heat process described by the following partial differential equation:

[0172]

[0173] Among them, represents the temperature function related to the spatial dimension x ∈ [0, X] and the time dimension, and u (x,t) represents the external input. In addition, from an engineering perspective, due to the limitations of the chemical reactor components, the structural model of the heat exchange process often exhibits time-varying characteristics; a (i,j) and b (i,j) are parameters with time-varying characteristics, representing the exchange gain in the heat exchange process.

[0174] Define It can be obtained that:

[0175]

[0176] If b (i,j) = 0, it can be approximately transformed into the following equation:

[0177]

[0178] The following networked two-dimensional system FM-II model can be obtained:

[0179]

[0180] Consider the following given parameters:

[0181] a (i,j) = sin(i + j) - 4, Δt = 0.1, Δx = 0.4,

[0182]

[0183] The initial state of the system is:

[0184] x (i,j)= [4.3cos(j)sin(i) 3.9cos(i - 1)sin(j)] T , (i ∈ [0 50], j = 0);

[0185] x (i,j) = [4.1sin(i)cos(j + 1) 4.5cos(i + 1)sin(j - 1)] T , (i = 0, j ∈ [1 50]);

[0186] Saturation threshold δ (i,j) = 0.6, assuming the variance of the process noise is W = 0.8I, (i, j ∈ [0 30]), the measurement outliers are random noise with mean 0 and variance 10I, and occur at times (15, 15), (23, 23), (29, 29);

[0187] Consider the nonlinear function as f(x (i,j) ) = 0.4sin(-x (i,j) ) + 0.2x (i,j) , and G 1,(i,j) = G 2,(i,j) = 0.2;

[0188] Consider using the following positive scalar λ 1 = 2, λ 2 = 3, R 1 = R 2 = 0.2 and φ 0 = 1.35;

[0189] Assume the number of redundant channels N = 2, and C 1,(i,j) = C 2,(i,j) = diag{0.35, 0.35 + 0.1sin(i + j)}, and the success rate of data packet transmission is and

[0190] The following partial observer gains can be calculated through the LMI toolbox in MATLAB software:

[0191]

[0192] The specific simulation graphs are as shown in the appendix Figures 2 - 7 as follows, Figure 2 and Figure 3 represent the trajectory of the system state x (i,j) and its observer estimate value trajectory, Figure 4 represents the trajectory of the estimation error e (i,j) , Figure 5 represents the trajectory of the saturation threshold δ (i,j) trajectory, fromFigures 2 - 5 It can be seen that the observer estimate can track the actual state x well (i,j) during its evolution, which indicates that the estimation of the proposed outlier-resistant proportional-integral observer can effectively track the actual state of the system. Figure 6 and Figure 7 Figure 9 shows the trajectory comparison effect between the outlier-resistant proportional-integral observer and the traditional proportional-integral observer. It can be seen that, compared with the traditional proportional-integral observer, the proposed outlier-resistant proportional-integral observer can effectively suppress the influence of measurement outliers on the observer.

[0193] Considering the existence of multiple influencing factors such as nonlinear factors, external disturbances, and randomly occurring measurement outliers, a new saturation function evolution rule based on two-way evolution is proposed in the method of designing the observer to suppress the influence of measurement outliers on the normal performance of the system. From the simulation results, the system state and its estimated trajectory diagram are clearly obtained, which further verifies the feasibility and applicability of the proportional-integral observer constructed in this embodiment.

[0194] A design system of an outlier-resistant proportional-integral observer for a networked two-dimensional system based on a redundant channel protocol, based on a design method of an outlier-resistant proportional-integral observer for a networked two-dimensional system based on a redundant channel protocol, includes a state space model construction module for a networked two-dimensional discrete system, a redundant channel measurement output module, an outlier-resistant proportional-integral observer structure design module, an augmented dynamic estimation error system establishment module, an observer gain solution module, and a state tracking module;

[0195] The state space model construction module for a networked two-dimensional discrete system is used to establish a state space model of a networked two-dimensional discrete system with nonlinear factors and external disturbances, and preliminarily model the state vector of the system, the process noise existing in the system, and the nonlinear terms.

[0196] The redundant channel measurement output module is used to construct a redundant channel measurement output with two-way evolution characteristics, and when a data packet loss phenomenon occurs in the main channel, the backup channel takes over the main channel to transmit the measurement data signal.

[0197] The outlier-resistant proportional-integral observer structure design module is used to design an outlier-resistant proportional-integral observer structure with an adaptive saturation function, and give the parameters of the designed observer gain matrix.

[0198] The augmented dynamic estimation error system establishment module is used to define the estimated value and estimation error of the state vector of the system, define the augmented vector, comprehensively consider the influence of measurement outliers and the redundant channel mechanism on the networked two-dimensional system, and transform the networked two-dimensional discrete system into an augmented dynamic estimation error system.

[0199] An observer gain solving module, which is used to introduce system performance evaluation indicators, substitute the designed observer gain matrix parameters into the augmented dynamic estimation error system, determine whether the augmented dynamic estimation error system meets the performance index constraints of being bounded in the mean square sense over a finite time domain, solve the proportional-integral observer gain matrix, and obtain the final robust proportional-integral observer structure;

[0200] A state tracking module, which is used to perform state tracking on the networked two-dimensional discrete system by using the obtained final robust proportional-integral observer structure.

[0201] A computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, a method for designing a robust proportional-integral observer for a networked two-dimensional system based on a redundant channel protocol is implemented.

[0202] A processing terminal, including a memory and a processor. A computer program that can run on the processor is stored in the memory. When the processor executes the computer program, a method for designing a robust proportional-integral observer for a networked two-dimensional system based on a redundant channel protocol is implemented.

[0203] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and reference can be made to the method part for the relevant parts.

[0204] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A design method for a networked two-dimensional system anti-outlier proportional-integral observer based on a redundant channel protocol, characterized in that: The following steps are involved: S1. Establish a state space model of a networked two-dimensional discrete system with nonlinear factors and external disturbances, and preliminarily model the state vector of the system, the process noise and nonlinear terms in the system; S2. Construct redundant channel measurement output with bidirectional evolution characteristics. When data packet loss occurs in the main channel, the backup channel takes over the main channel to transmit the measurement data signal; S3. Design a wild value resistant proportional integral observer structure with an adaptive saturation function, and give the designed observer gain matrix parameters; S4. Define the estimated value and estimated error of the state vector of the system, define the augmented vector, comprehensively consider the impact of the measured wild value and the redundant channel mechanism on the networked two-dimensional system, and transform the networked two-dimensional discrete system of step S1 into an augmented dynamic estimation error system; S5. Introduce the system performance evaluation index, substitute the designed observer gain matrix parameters into the augmented dynamic estimation error system in step S4, and judge whether the augmented dynamic estimation error system satisfies the finite time domain boundedness in the mean square sense. If the performance index constraint is satisfied, the system design is terminated to obtain the final anti-outlier proportional integral observer structure; Otherwise, repeat steps S3 to S5; S6. Using the obtained final outlier-resistant proportional integral observer structure to track the state of the networked two-dimensional discrete system; The state space model of the networked two-dimensional discrete system in step S1 is: x (i+1,j+1) =A 1，(i+1,j) x (i+1,j) +A 2,(i,j+1) x (i,j-1) +F 1，(i+1,j) f(x (i+1,j) )+F 2，(i，j+1) f(x (i,j+1) )+B 1,(i+1，j) ω (i+1，j) +B 2，(i,j+1) ω (i,j+1) in, is the state vector of the networked two-dimensional system, The networked two-dimensional system is subjected to process noise with zero mean and variance W, n x is the dimension of the system state vector, n ω is the dimension of the input vector, and is a time-varying system matrix of known dimension, y(x, (i，j) ) is the smooth nonlinear factor existing in the networked two-dimensional system; The redundant channel measurement output with bidirectional evolution characteristics constructed in step S2 is specifically: in, r∈{1,2,...,N},y r，(i，j) is the output of the rth measurement channel at time (i, j), N is the number of redundant channels in the networked two-dimensional system, and is a known time-varying matrix; According to the uncertainty and discontinuity of packet loss, a random variable σ that follows a Bernoulli distribution is defined. r,(i,j) To indicate whether the rth channel has packet loss at time (i, j), the value is 0 or 1, 0 means that the channel has packet loss, and 1 means that the channel has no packet loss: is a known constant representing the probability of packet loss in the rth channel; Reconstruct the redundant channel measurement output as: y (i，j) =Φ (i，j) C (i，j) x (i，j) +D (i，j) oh (i，j) ; in, If the random variable σ 1,(i,j) =1, no packet loss occurs on the primary channel and the redundant channel will not be activated; if the random variable σ m(i，j) =1 and σ r，(i，j) =0, m∈[2,N], r∈[1,m-1], then packet loss occurs in the r-1th channel, and normal data packets will be transmitted through the rth channel; The structure of the anti-outlier proportional integral observer with adaptive saturation function designed in step S3 is specifically: in, is the system state vector x (i，j) The estimated value of The measured output y (i，j) Rather than estimating The weighted error between and is the designed proportional-integral observer gain matrix parameter, is a nonlinear saturation function; Nonlinear saturation function Specifically: in, is the sth vector in the saturation function, and the saturation threshold δ (i，j) is a positive scalar, according to the measured output y (i，j) With its estimated value The error between them is adaptively adjusted; δ (i，j) The specific evolution process is: Among them, α1, α2∈[0, 1 / 2) are weight coefficients, and is a positive definite symmetric matrix of appropriate dimension.

2. The design method of a networked two-dimensional system anti-outlier proportional-integral observer based on a redundant channel protocol according to claim 1 is characterized in that: For step S4: Define the state vector x of the networked two-dimensional system (i,j) With its estimated value The error between The weighted error is χ (i，j) , let n = 2n x +n δ , construct the augmented matrix: Then, the augmented dynamic estimation error system is specifically: in, m∈[2,N].

3. The design method of a networked two-dimensional system anti-outlier proportional-integral observer based on a redundant channel protocol according to claim 1, characterized in that: Step S5 also includes using Lyapunov stability theory and linear matrix inequality analysis method to obtain sufficient conditions for the augmented dynamic estimation error system to satisfy finite time domain boundedness in the mean square sense and the existence of proportional integral observer and solve the observer gain matrix.

4. The design method of a networked two-dimensional system anti-outlier proportional-integral observer based on a redundant channel protocol according to claim 2, characterized in that: The system performance evaluation index introduced in step S5 is: If there exists a finite time domain function And the augmented dynamic estimation error system η (i,j) The following constraints are met: Then the augmented dynamic estimation error system η (i,j) It is considered to be bounded in a finite time domain in the sense of mean square, where E{·} represents the mean of a certain variable and π0 represents a preset upper bound; The sufficient condition for the augmented dynamic estimation error system to be bounded in finite time domain in the sense of mean square is: To solve, if there exists a positive symmetric matrix P (i+1,j+1) , R (i+1,j+1) ,P(i+1,j),R(i,j+1),Q 1,(i+1,j) and Q 2,(i,j+1) , and a matrix of appropriate dimension and If the sufficient condition inequality holds, the system is bounded in finite time domain in the sense of mean square under the influence of measurement wild values ​​and redundant channel protocols, and the system estimate can track the system state; The proportional integral observer gain matrix to be solved is:

5. A networked two-dimensional system anti-outlier proportional-integral observer design system based on redundant channel protocol, characterized in that: A method for designing a networked two-dimensional system anti-wild value proportional integral observer based on a redundant channel protocol according to any one of claims 1 to 4, comprising a networked two-dimensional discrete system state space model building module, a redundant channel measurement output module, an anti-wild value proportional integral observer structure design module, an augmented dynamic estimation error system establishment module, an observer gain solution module and a state tracking module; The networked two-dimensional discrete system state space model building module is used to establish a networked two-dimensional discrete system state space model with nonlinear factors and external disturbances, and to perform preliminary modeling of the system's state vector, process noise and nonlinear terms in the system; The redundant channel measurement output module is used to construct a redundant channel measurement output with bidirectional evolution characteristics. When data packet loss occurs in the main channel, the backup channel takes over the main channel to transmit the measurement data signal; The outlier-resistant proportional-integral observer structure design module is used to design an outlier-resistant proportional-integral observer structure with an adaptive saturation function and provide the designed observer gain matrix parameters; The augmented dynamic estimation error system establishment module is used to define the estimated value and estimation error of the system's state vector, define the augmented vector, comprehensively consider the impact of measurement wild values ​​and redundant channel mechanisms on the networked two-dimensional system, and transform the networked two-dimensional discrete system into an augmented dynamic estimation error system; The observer gain solution module is used to introduce the system performance evaluation index, substitute the designed observer gain matrix parameters into the augmented dynamic estimation error system, judge whether the augmented dynamic estimation error system meets the performance index constraint of finite time domain in the mean square sense, solve the proportional integral observer gain matrix, and obtain the final anti-outlier proportional integral observer structure; The state tracking module is used to track the state of the networked two-dimensional discrete system by using the final anti-outlier proportional integral observer structure obtained.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for designing a networked two-dimensional system anti-outlier proportional-integral observer based on a redundant channel protocol as described in any one of claims 1 to 4 is implemented.

7. A processing terminal, comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, characterized in that: When the processor executes the computer program, the method for designing a networked two-dimensional system anti-outlier proportional-integral observer based on a redundant channel protocol as described in any one of claims 1 to 4 is implemented.

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