A fixed-time predictive sliding mode control method for hypersonic aircraft based on particle filter
Through the particle filter and fixed-time predictive sliding mode control method, the problem of poor control effect of hypersonic aircraft under random gust interference is solved, and the system's rapid stability and high-precision control are achieved.
Patent Information
- Application Number
- CN202510978583.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-16
- Publication Date
- 2025-09-16
- Estimated Expiration
- 2045-07-16
AI Technical Summary
Existing hypersonic aircraft control systems have poor control effects when facing random gust interference, especially during high-speed flight, which is easily affected by meteorological factors and sensor measurement errors, resulting in a decrease in convergence speed and accuracy.
A fixed-time predictive sliding mode control method based on particle filter is adopted. By constructing the state equation of the disturbed system, the particle filter is used for state estimation, and a fixed-time reaching law is designed. Combined with the double-power reaching law and the rolling optimization strategy, the actuator chattering is weakened to ensure that the system converges quickly and tracks the reference trajectory.
Rapid and stable control of hypersonic aircraft under non-Gaussian random interference is achieved, the stability errors of attitude angle and attitude angular rate are significantly reduced, the system convergence speed and accuracy are improved, and the impact of gust interference is effectively weakened.
Smart Images
Figure CN120469253B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of aircraft control, and in particular to a fixed-time predictive sliding mode control method for a hypersonic aircraft based on a particle filter. Background Art
[0002] Hypersonic vehicles (Hypersonic vehicles) are winged or wingless aircraft, such as aircraft, missiles, and artillery shells, that fly at speeds exceeding five times the speed of sound. They exhibit strong nonlinearity and strong coupling, and operate in highly complex environments. These factors present numerous challenges in the design and application of flight control systems for hypersonic vehicles. Especially during high-speed flight, Hypersonic vehicles are susceptible to meteorological interference and sensor measurement errors, resulting in reduced control system convergence speed and accuracy. Random gust disturbances are a common form of meteorological disturbances, and their randomness and suddenness pose a severe challenge to the aircraft's attitude control system. Therefore, effectively mitigating or eliminating the impact of random gust disturbances is crucial for ensuring flight stability and control accuracy in practical flight control systems. Existing research on random disturbances relies heavily on white noise simulations for aircraft anti-disturbance control, ignoring the sudden nature of gust disturbances. Summary of the Invention
[0003] Objective of the invention: The objective of the present invention is to provide a fixed-time predictive sliding mode control method for a hypersonic aircraft based on a particle filter for processing random gust interference.
[0004] Technical solution: A fixed-time predictive sliding mode control method for a hypersonic aircraft based on a particle filter, comprising the following steps:
[0005] S1. Add process noise to the input end of the hypersonic aircraft system and measurement noise to the output end of the hypersonic aircraft system, construct the state equation of the disturbed system, and use a particle filter to obtain the filtered state of the disturbed system;
[0006] S2. Under the undisturbed system state, the system discrete state space equation is selected as the prediction model to predict the sliding surface, and a fixed-time reaching law is designed. The fixed-time predictive sliding mode reaching law is obtained using the fixed-time reaching law.
[0007] S3. Using the filtered state of the disturbed system in step S1 to replace the undisturbed system state in step S2, a fixed-time predictive sliding mode controller is obtained.
[0008] Specifically, in step S1, the process noise and measurement noise of the hypersonic aircraft system both conform to Gaussian mixture distribution.
[0009] Specifically, the above Gaussian mixture distribution complies with the following probability density function:
[0010] ,
[0011] Where: is the probability density function, is the set of parameters of all mixture components, For the sample, For expectations, is the covariance matrix, is the data dimension.
[0012] Specifically, in step S1, the state equation of the disturbed system is:
[0013] ,
[0014] Where: is the state vector of the disturbed system, is the output vector of the disturbed system, is the control output vector of the disturbed system, is the state vector of the disturbed system at the previous moment, is the process noise, To measure noise, 、 、 is the matrix of the nominal disturbed system dynamics.
[0015] Specifically, in step S2, the system discrete state space equation is:
[0016] ,
[0017] Where: is the undisturbed system state vector, is the undisturbed system output vector, is the system control output vector, represents the kth sampling moment of the discrete system, 、 、 is the matrix of the nominally undisturbed system dynamics.
[0018] Specifically, in step S2, the fixed time convergence law is:
[0019] ,
[0020] Where: is the design parameter, 、 、 is the power exponent, is a symbolic function, is the error between the predicted output of the system after correction and the reference trajectory of the system.
[0021] Specifically, in step S2, the fixed-time prediction sliding mode reaching law is calculated as follows: according to the discrete state space equation of the system, the sliding surface is designed using the error between the predicted output after system correction and the reference trajectory of the system, and then the designed fixed-time convergence reaching law is discretized to obtain the fixed-time sliding mode reaching law in the prediction time domain. Then, the optimization function and performance index function are designed, and after solving the optimization function to obtain the reference input, the performance index function is solved using the reference input to obtain the fixed-time prediction sliding mode reaching law.
[0022] Specifically, the sliding surface is:
[0023] ,
[0024] Where: is the sliding surface, is a constant matrix, is the predicted output after system correction, is the system reference trajectory, Represents the kth sampling moment of the discrete system;
[0025] Then the sliding mode surface of the discrete system at the k+i sampling moment is obtained as:
[0026] ,
[0027] ,
[0028] ,
[0029] ,
[0030] ,
[0031] Where: is the set value, is the actual output vector of the system, is the softening coefficient, is the discrete system sampling time, is the expected closed-loop response time of the reference trajectory, 、 and For the operator.
[0032] Specifically, the fixed-time sliding mode reaching law in the prediction time domain is:
[0033] ,
[0034] Where: To predict the fixed-time sliding mode reaching law in the time domain, Represents the k+ith sampling moment of the discrete system;
[0035] The optimization function is:
[0036] ,
[0037] Where: is the initial time of the prediction domain, is the end time of the prediction time domain, is the reference input, 、 is the weight matrix;
[0038] The performance indicator function is:
[0039] ,
[0040] Where: is the performance indicator function, is the actual input, 、 is the weight matrix;
[0041] when When , we get the fixed time prediction sliding mode reaching law:
[0042] ,
[0043] Where: It is a sliding mode reaching law for fixed time prediction.
[0044] Specifically, in step S3, the system state space expression after particle filtering is:
[0045] ,
[0046] Where: is the system state vector after particle filtering, is the actual output vector of the system, is the system control output vector, 、 、 is the matrix of the nominally undisturbed system dynamics, represents the kth sampling moment of the discrete system.
[0047] Beneficial Effects: Compared with existing technologies, this invention demonstrates significant advantages: It addresses the mechanism of random interference experienced by hypersonic vehicles and utilizes Gaussian mixture-distributed noise to simulate the suddenness and randomness of external environmental interference. Furthermore, a novel fixed-time convergence law, based on the bi-power convergence law, is designed. This approach not only ensures rapid system convergence but also mitigates actuator chatter. The sliding surface is designed using the error between the system's corrected predicted output and the system's reference trajectory, ensuring that the system's trajectory continuously approaches the sliding surface and converges within a fixed time. In order to ensure that the actual output of the system has good tracking performance for the reference trajectory while processing input constraints, the present invention designs a two-level optimization strategy based on the rolling optimization method in model predictive control. First, an optimization problem is solved to obtain a reference input, and then the reference input is introduced into the performance index function considering the control input. Then, the performance index function in the optimization time domain is solved to obtain the control law at each moment in the time domain. After obtaining the fixed-time predictive sliding mode control law, the system state after particle filtering is used to replace the system state in the interference-free condition, thereby obtaining a fixed-time predictive sliding mode controller based on the particle filter, thereby solving the problem that the predictive sliding mode control has poor control effect under non-Gaussian distribution random interference, and realizing fast and stable control of hypersonic aircraft under random interference. BRIEF DESCRIPTION OF THE DRAWINGS
[0048] Figure 1 It is a flow chart of the method of the present invention.
[0049] Figure 2 It is a graph of the slow loop noise amplitude and probability density function of the present invention.
[0050] Figure 3 It is a graph of the fast loop noise amplitude and probability density function of the present invention.
[0051] Figure 4 2 is a comparison diagram of the angle of attack response of the present invention.
[0052] Figure 5 2 is a comparison diagram of the sideslip angle response of the present invention.
[0053] Figure 6 2 is a comparison diagram of the roll angle response of the present invention.
[0054] Figure 7 2 is a comparison diagram of the roll angular rate response of the present invention.
[0055] Figure 8 2 is a comparison diagram of the pitch angle rate response of the present invention.
[0056] Figure 9 This is a comparison diagram of the yaw rate response of the present invention. DETAILED DESCRIPTION
[0057] A preferred embodiment of the present invention is further described below with reference to the accompanying drawings.
[0058] Example 1
[0059] See also Figure 1 As shown, this embodiment provides a fixed-time predictive sliding mode control method for a hypersonic aircraft based on a particle filter, comprising the following steps:
[0060] S1. Equivalently treat the random gust interference in the motion of a hypersonic aircraft as the process noise of the system and add it to the system input. Equivalently treat the measurement error of the hypersonic aircraft sensor as the measurement noise of the system and add it to the system input. The state equation of the disturbed system is constructed and the filtered state of the disturbed system is obtained using a particle filter.
[0061] In this embodiment, a Gaussian mixture distribution model is used to simulate gust interference and sensor measurement error. When the sample data x is multidimensional data, the Gaussian mixture distribution complies with the following probability density function:
[0062] ,
[0063] Where: is the probability density function, is the set of parameters of all mixture components, For the sample, For expectations, is the covariance matrix, is the data dimension.
[0064] The state equation of the disturbed system is selected as:
[0065] ,
[0066] Where: is the state vector of the disturbed system, is the output vector of the disturbed system, is the control output vector of the disturbed system, is the state vector of the disturbed system at the previous moment, is the process noise, is the measurement noise, process noise and measurement noise are all random interference noises that obey the above Gaussian mixture distribution. 、 、 is the matrix of the nominal disturbed system dynamics.
[0067] Particle filter design:
[0068] The particle filter is a recursive Bayesian filtering technique based on the Monte Carlo method. It estimates the system state by recursively updating the posterior probability distribution of the state through the Bayesian theorem. Specifically, it includes the following steps:
[0069] (1) Distribution from the initial state of the system sampling particles :
[0070] ,
[0071] Initialize uniform weights :
[0072] ,
[0073] (2) Prediction status:
[0074] Use the state transfer equation to propagate to each particle:
[0075] ,
[0076] The process noise Sampling from a GMM.
[0077] The sampling process is as follows:
[0078] First, define the probability density function of the Gaussian mixture distribution model as follows :
[0079] ,
[0080] Where: is the number of mixed Gaussian components, It is Gaussian component weights, and satisfy , It is Gaussian distribution with mean , the covariance matrix is .
[0081] Then sample the process noise from the GMM:
[0082] Generate a uniformly distributed random number .
[0083] Choose a Gaussian component based on:
[0084] if , then select the first Gaussian distribution .
[0085] if , then choose the second Gaussian distribution .
[0086] And so on, until you find satisfaction of .
[0087] Sample from a chosen Gaussian distribution:
[0088] .
[0089] Finally, for each particle , the status update process is as follows:
[0090] .
[0091] (3) Calculate weight:
[0092] Calculate the weight of each particle based on the observed value:
[0093] ,
[0094] The likelihood function Determined by the measurement equation:
[0095] ,
[0096] Normalized weights:
[0097] ,
[0098] The system measurement equation is:
[0099] ,
[0100] The measurement noise Obey Gaussian mixture distribution:
[0101] ,
[0102] Given a particle and observation , calculate the likelihood function:
[0103] ,
[0104] Where: is the dimension of the measurement noise, is the Gaussian component The determinant of the covariance matrix of .
[0105] (4) Update particle weights:
[0106] The particle filter weights are updated as:
[0107] ,
[0108] Substituting the likelihood function into the above formula, we get:
[0109] ,
[0110] Then normalize:
[0111] .
[0112] (5) Resampling:
[0113] Since particle weights may be concentrated on a few particles, resampling is required to avoid particle degradation. Using the system resampling method, N particles are resampled from the current particle set, making it easier for high-weight particles to be selected. The new weights of all particles are equal:
[0114] ,
[0115] Then repeat steps (2)-(5) until the k+pth moment.
[0116] (6) State estimation:
[0117] Compute an estimate of the system state using a weighted sum of particles:
[0118] .
[0119] That is, the filtered state of the disturbed system is obtained through the particle filter.
[0120] S2. Under the undisturbed system state, the system discrete state space equation is selected as the prediction model to predict the sliding surface, and a fixed-time reaching law is designed. The fixed-time prediction sliding mode reaching law is obtained using the fixed-time reaching law.
[0121] On the basis of the bi-power reaching law, the present invention designs a fixed-time reaching law, which not only ensures the rapid convergence of the system but also weakens the chattering of the actuator.
[0122] The fixed time reaching law is designed as follows:
[0123] ,
[0124] Where: is the design parameter, 、 、 is the power exponent, is a symbolic function, is the error between the predicted output of the system after correction and the reference trajectory of the system.
[0125] Design and predict the sliding surface at time k+p:
[0126] The system discrete state space equation is selected as the prediction model:
[0127] ,
[0128] Where: is the undisturbed system state vector, is the undisturbed system output vector, is the system control output vector, represents the kth sampling moment of the discrete system, 、 、 is the matrix of the nominally undisturbed system dynamics.
[0129] In order to ensure that the motion trajectory of the system continuously approaches the sliding surface and guarantees fixed time convergence, the sliding surface is designed using the error between the predicted output after system correction and the system reference trajectory. The sliding surface at the kth moment can be designed as:
[0130] ,
[0131] Where: is the sliding surface, is a constant matrix, is the predicted output after system correction, is the system reference trajectory, Represents the kth sampling moment of the discrete system;
[0132] Then the sliding mode surface of the discrete system at the k+i sampling moment is obtained as:
[0133] ,
[0134] ,
[0135] ,
[0136] ,
[0137] ,
[0138] Where: is the set value, is the actual output vector of the system, is the softening coefficient, is the discrete system sampling time, is the expected closed-loop response time of the reference trajectory, 、 and For the operator.
[0139] Discretize the designed fixed-time reaching law and obtain the following formula:
[0140] ,
[0141] After simplification, we get:
[0142] ,
[0143] Where: To predict the fixed-time sliding mode reaching law in the time domain, Represents the k+ith sampling moment of the discrete system.
[0144] After obtaining the fixed-time sliding mode reaching law in the prediction time domain, in order to ensure that the actual output of the system has good tracking performance on the reference trajectory while processing the input constraints, the present invention designs a two-level optimization strategy based on the rolling optimization method in model predictive control. First, the reference input is obtained by solving an optimization problem. , then bring the reference input into the performance index function considering the control input, and then solve the optimization time domain The performance index function within the time domain is obtained to obtain the control law at each moment in the time domain.
[0145] Define the optimization function as:
[0146] ,
[0147] Where: is the initial time of the prediction domain, is the end time of the prediction time domain, is the reference input, 、 is the weight matrix;
[0148] The performance indicator function is:
[0149] ,
[0150] Where: is the performance indicator function, is the actual input, i.e. the fixed time prediction sliding mode reaching law, 、 is the weight matrix.
[0151] when When , we get the fixed time prediction sliding mode reaching law:
[0152] ,
[0153] Where: It is a sliding mode reaching law for fixed time prediction.
[0154] S3. Using the filtered state of the disturbed system in step S1 to replace the undisturbed system state in step S2, a fixed-time predictive sliding mode controller is obtained.
[0155] The state space expression of the system after particle filtering is:
[0156] ,
[0157] Where: is the system state vector after particle filtering, is the actual output vector of the system, is the system control output vector, 、 、 is the matrix of the nominally undisturbed system dynamics, represents the kth sampling moment of the discrete system.
[0158] The new state after particle filtering is applied to the design of fixed-time predictive sliding mode controller, thus obtaining a new fixed-time predictive sliding mode controller based on particle filter. :
[0159] .
[0160] The present invention starts from the external environmental interference of hypersonic aircraft, simulates non-Gaussian random interference through a mixed Gaussian distribution model, and then studies the problem of aircraft attitude control under random gust interference; proposes a fixed-time predictive sliding mode control method based on a particle filter to solve the problem of poor control effect of the predictive sliding mode control method when facing random gust interference, thereby realizing effective control of the system under non-Gaussian distribution random interference.
[0161] The fixed-time predictive sliding mode control method for a hypersonic aircraft based on a particle filter is now applied in a specific scenario.
[0162] In this embodiment, a hypersonic aircraft is taken as the controlled object. First, the system is divided into fast and slow loops based on time-scale separation. Then, the fast and slow loop system models are linearized according to the small disturbance principle. On this basis, a fast and slow loop controller is designed.
[0163] Select the actual disturbed hypersonic aircraft model:
[0164] The slow loop model is:
[0165] ,
[0166] The fast loop model is:
[0167] ,
[0168] Where: In slow loop state, In fast loop state, 、 are process noise and measurement noise that obey Gaussian mixture distribution respectively; and are the linear model coefficient matrices for the slow loop and the fast loop respectively;
[0169] , specifically:
[0170] ,
[0171] , specifically:
[0172] ,
[0173] ,
[0174] ,
[0175] Where: is the mass of the aircraft, is the wingspan length, is the mean aerodynamic chord length, is the length between the center of mass and the center of reference moment, are aerodynamic parameters, where ; ; is the pitching moment, is the yaw moment, is the rolling moment, represents the lift coefficient, represents the lateral force coefficient, is the drag coefficient, is the acceleration due to gravity, is the flight speed, is the angle of attack, is the sideslip angle, is the tilt angle, is the roll angle, is the roll angular rate, is the pitch angular rate, is the yaw angular rate, For thrust, is the airfoil reference area, is the dynamic pressure, is the inertia tensor, 、 、 are the moments of inertia about the x-axis, y-axis, and z-axis respectively.
[0176] Since both the slow-loop model and the fast-loop model are MIMO systems (multiple-input, multiple-output systems), the controller design can be performed based on the above-mentioned state equation of the disturbed system.
[0177] To verify the effectiveness of the present invention, the above method was simulated on the MATLAB / Simulink simulation platform and corresponding simulation results were obtained. Table 1 below lists the aircraft parameters used in the simulation.
[0178] Table 1
[0179]
[0180] Table 2 below shows the controller parameters used in the simulation calculation.
[0181] Table 2
[0182]
[0183] Table 3 below shows the parameters used in the Gaussian mixture distribution model. Figure 2 is the amplitude and probability density function of the non-Gaussian noise added to the slow loop, Figure 3 is the amplitude and probability density function of the non-Gaussian noise added to the fast loop.
[0184] Table 3
[0185]
[0186] The simulation results are numerically analyzed and the Figures 4 to 9 , Figure 4 This is a comparison chart of angle of attack response. Figure 5 is the comparison chart of sideslip angle response, Figure 6 is the roll angle response comparison chart, Figure 7 This is a comparison chart of roll angular rate response. Figure 8 This is a comparison chart of pitch angle rate response. Figure 9 This is a comparison chart of yaw rate response. Figures 4 to 9 In each figure, sub-graph (a) is the simulation result without the control method of the present invention, and sub-graph (b) is the simulation result with the control method of the present invention. From the above analysis and comparison, it can be seen that although the noise amplitude is not large, the interference caused by the noise has a great impact on the high-speed moving aircraft. Under the control method of the present invention, the aircraft attitude angle stability error is [-0.02, 0.02], and the attitude angular rate stability error is [-5×10 -4 ,5×10 -4 ], which is significantly improved compared with the previous unfiltered results, with a very small error range and can be considered stable. In addition, Figures 4 to 9 It can also be seen that the control method of the present invention significantly improves the convergence speed and accuracy of various system parameters. In summary, the control method provided by the present invention can ensure that the attitude angle response of a hypersonic aircraft quickly reaches the desired state and the attitude angular rate response converges quickly when faced with strong impulsive noise interference such as Gaussian mixture distribution. Simulation results verify the effectiveness of the control method of the present invention.
Claims
1. A fixed-time predictive sliding mode control method for a hypersonic aircraft based on a particle filter, characterized in that: The following steps are involved: S1. Add process noise to the input end of the hypersonic aircraft system and measurement noise to the output end of the hypersonic aircraft system, construct the state equation of the disturbed system, and use a particle filter to obtain the filtered state of the disturbed system; S2. Under the undisturbed system state, the system discrete state space equation is selected as the prediction model to predict the sliding surface, and a fixed-time reaching law is designed. The fixed-time predictive sliding mode reaching law is obtained using the fixed-time reaching law. The fixed-time convergence law is: ， Where: is the design parameter, 、 、 is the power exponent, is a symbolic function, is the error between the predicted output after system correction and the system reference trajectory; The fixed-time prediction sliding mode reaching law is calculated as follows: according to the discrete state space equation of the system, the sliding surface is designed using the error between the predicted output after the system correction and the reference trajectory of the system, the designed fixed-time convergence reaching law is discretized to obtain the fixed-time sliding mode reaching law in the prediction time domain, and then an optimization function and a performance index function are designed. After solving the optimization function to obtain a reference input, the performance index function is solved using the reference input to obtain the fixed-time prediction sliding mode reaching law. The fixed-time sliding mode reaching law in the prediction time domain is: ， Where: To predict the fixed-time sliding mode reaching law in the time domain, represents the k+ith sampling moment of the discrete system, is the discrete system sampling time, is the sliding surface; The optimization function is: ， Where: is the initial time of the prediction domain, is the end time of the prediction time domain, is the reference input, 、 is the weight matrix, is the system reference trajectory, is the actual output vector of the system; The performance indicator function is: ， Where: is the performance indicator function, is the actual input, 、 is the weight matrix; when When , we get the fixed time prediction sliding mode reaching law: ， Where: is the sliding mode reaching law for fixed-time prediction, is a constant matrix, is the undisturbed system state vector, 、 and is the operator, is the set value; S3. Using the filtered state of the disturbed system in step S1 to replace the undisturbed system state in step S2, a fixed-time predictive sliding mode controller is obtained.
2. The particle filter-based fixed-time predictive sliding mode control method for hypersonic aircraft according to claim 1, characterized in that: In step S1, the process noise and measurement noise of the hypersonic aircraft system both conform to Gaussian mixture distribution.
3. The particle filter-based fixed-time predictive sliding mode control method for hypersonic aircraft according to claim 2, characterized in that: The Gaussian mixture distribution follows the following probability density function: ， Where: is the probability density function, is the set of parameters of all mixture components, For the sample, For expectations, is the covariance matrix, is the data dimension.
4. The particle filter-based fixed-time predictive sliding mode control method for hypersonic aircraft according to claim 1, characterized in that: In step S1, the state equation of the disturbed system is: ， Where: is the state vector of the disturbed system, is the output vector of the disturbed system, is the control output vector of the disturbed system, is the state vector of the disturbed system at the previous moment, is the process noise, To measure noise, 、 、 is the matrix of the nominal disturbed system dynamics.
5. The particle filter-based fixed-time predictive sliding mode control method for hypersonic aircraft according to claim 1, characterized in that: In step S2, the system discrete state space equation is: ， Where: is the undisturbed system output vector, represents the kth sampling moment of the discrete system, 、 、 is the matrix of the nominally undisturbed system dynamics.
6. The particle filter-based fixed-time predictive sliding mode control method for hypersonic aircraft according to claim 5, characterized in that: The sliding surface is: ， Where: is the predicted output after system correction, Represents the kth sampling moment of the discrete system; Then the sliding mode surface of the discrete system at the k+i sampling moment is obtained as: ， ， ， ， ， Where: is the softening coefficient, is the expected closed-loop response time of the reference trajectory.
7. The particle filter-based fixed-time predictive sliding mode control method for hypersonic aircraft according to claim 1, characterized in that: In step S3, the system state space expression after particle filtering is: ， Where: is the system state vector after particle filtering, 、 、 is the matrix of the nominally undisturbed system dynamics, represents the kth sampling moment of the discrete system.