A Neural Adaptive Sliding Mode Observer Design Method for Fault Estimation in Satellite Attitude Control Systems

Abstract

The present invention relates to the technical field of spacecraft fault diagnosis, and specifically discloses a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation, including taking into account concurrent actuator, sensor faults and constraints, performing equivalent transformation on the attitude control system; establishing a continuous time constrained equivalent uncertainty description system; adding a fuzzification layer and a fuzzy reasoning layer to a hyperbasis function neural network to obtain an expression for uncertainty obtained by the fuzzy hyperbasis function neural network; designing a neural adaptive sliding mode observer based on an improved fuzzy hyperbasis function neural network, solving the observer gain matrix using linear matrix inequalities, and achieving better concurrent fault estimation based on better uncertainty estimation. The present invention adopts the above-mentioned neural adaptive sliding mode observer design method for satellite attitude control system fault estimation, solves the concurrent fault estimation problem of the satellite attitude control system under complex constraints, and improves the accuracy of fault estimation.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft fault diagnosis, and in particular to a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation. Background Art

[0002] Satellite attitude control systems (ACSs) are important subsystems of satellites. Satellites work in extreme environments such as high vacuum, multiple radiation, and extreme temperatures, which can easily cause failures in key components of ACSs, and it is difficult to repair the failures immediately. Therefore, when a satellite fails, timely and accurate fault diagnosis has great national defense and economic value. Furthermore, complex constraints such as uncertainty, external disturbances, and measurement noise caused by special working environments increase the difficulty of diagnosing concurrent faults of actuators and sensors of ACSs. ​​It is of great significance to combine intelligent methods and modern fault diagnosis technology to further improve the diagnostic accuracy of concurrent faults of ACSs under complex constraints, especially the concurrent fault estimation accuracy.

[0003] At present, adaptive observers based on residual evaluation functions, iterative learning observers based on online allocation control, and fuzzy disturbance observers have been used to estimate actuator faults and external disturbances in ACSs. ​​Fuzzy disturbance observers have been combined with adaptive sliding mode controllers to achieve fault-tolerant control of ACSs with actuator faults. Finite-time integral sliding mode disturbance observers have been combined with backstepping state variables and virtual controllers to estimate model uncertainties in ACSs. ​​Considering the strong ability of neural networks in approximating nonlinearity, neural adaptive fault estimation methods have been applied in ACSs. ​​Fuzzy neural adaptive observers combining RBF neural networks with TS fuzzy models have been used for actuator fault estimation. Using RBF neural networks to estimate uncertainty, neural adaptive sliding mode control strategies based on disturbance observers and fault estimators have been used for fault-tolerant control of flexible satellite methods. Neuro-adaptive sliding mode observers based on Chebyshev neural networks have been used to estimate multi-actuator faults, uncertainties, and external disturbances. However, if actuator and sensor failures occur concurrently, modeling based on state-space systems may lead to model errors.

[0004] Satellite ACSs can be modeled as descriptive systems by considering actuator and sensor concurrent failures as additional system variables, thereby realizing concurrent failure estimation based on descriptive systems. Descriptive systems have been combined with adaptive sliding mode observers to achieve accurate estimation of the upper bound of actuator failures in ACSs systems. Robust sliding mode observers and adaptive sliding mode controllers based on descriptive systems have been used for fault estimation and fault-tolerant control of ACSs systems. Furthermore, a neural adaptive sliding mode fault estimation method for fuzzy description systems has been proposed based on RBF neural networks. In addition, swarm intelligence optimization algorithms such as the improved whale optimization algorithm and the improved dwarf mongoose algorithm have been used to optimize the performance of neural networks to further improve the estimation accuracy of neural network, thereby improving the accuracy of concurrent failure estimation of ACSs based on descriptive systems.

[0005] Nevertheless, there are still some shortcomings in the design of ACSs fault estimation based on the description system, especially the neural adaptive sliding mode observer for ACSs fault estimation based on the description system. First, due to the singular structure of the description system, the design of its neural adaptive sliding mode observer easily leads to singular terms in the dynamic error term, which makes it difficult to solve the observer gain. Secondly, although fuzzy methods have been used to improve RBF neural networks and improve network performance, due to the structure of RBF neural networks, other neural network models still need to be improved to further improve the fault estimation performance based on the neural adaptive sliding mode observer. Finally, the existing swarm intelligence optimization algorithms generally have shortcomings in terms of convergence speed, optimization accuracy, and jumping out of local optimality, resulting in limited improvement of neural network performance by existing swarm intelligence optimization algorithms.

[0006] Therefore, the present invention considers the constraints of concurrent actuator and sensor failures and uncertainties, external disturbances, measurement noise and other constraints of satellite ACSs, and performs equivalent transformation on the attitude control system; regards actuator failures, sensor failures and measurement noise augmented variables as additional state variables of ACSs, and establishes a continuous time restricted equivalent uncertain description system; adds a fuzzification layer and a fuzzy reasoning layer to a hyperbasis function neural network (HBFNN) to obtain a fuzzy hyperbasis function neural network (FHBFNN); designs an adaptive sliding mode observer based on an improved fuzzy hyperbasis function neural network (IHBFNN-ASMO), including designing a description system state estimation term, an uncertainty estimation term based on an improved fuzzy hyperbasis function neural network; an improved neural sliding mode estimation term in the uncertainty estimation term and an improved sliding mode compensation term for network reconstruction error. The improvement method is: an improved black-winged kite algorithm (IBKA) is obtained by introducing an improved circular chaos map, and then the IBKA is used to dynamically optimize the basis function of the fuzzy neural network, the network weight estimation update law, and the network reconstruction error upper bound estimation update law to improve the approximation ability of the neural network to nonlinear uncertainty. The observer gain matrix is ​​solved by linear matrix inequality, and the proposed neural adaptive sliding mode observer is used to achieve better uncertainty estimation, concurrent fault estimation and satellite state (three-axis angle and angular velocity) estimation, which has important research significance. Summary of the invention

[0007] The purpose of the present invention is to provide a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation, thereby realizing high-precision fault estimation of the satellite attitude control system.

[0008] To achieve the above object, the present invention provides a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation, comprising the following steps:

[0009] S1. Consider concurrent actuator and sensor failures and uncertainties, external disturbances and measurement noise, and perform equivalent transformation on the satellite attitude control system; regard actuator failures, sensor failures and measurement noise augmented variables as additional state variables of the satellite attitude control system, and establish a continuous-time constrained equivalent uncertain description system;

[0010] S2. For the established restricted equivalent uncertain description system, a fuzzification layer and a fuzzy reasoning layer are added to the super basis function neural network to obtain a fuzzy super basis function neural network to obtain an uncertain fuzzy super basis function neural network expression;

[0011] Design a neural adaptive sliding mode observer with an estimation term describing the system state and an uncertainty estimation term based on an improved fuzzy hyperbasis function neural network;

[0012] Design an improved neural sliding mode estimation term in the uncertainty estimation term based on the improved fuzzy hyperbasis function neural network and an improved sliding mode compensation term for network reconstruction error;

[0013] Improved neural sliding mode estimation term and improved sliding mode compensation term of network reconstruction error. The specific improvement methods are: using the improved circular chaos mapping method to improve the black kite algorithm, and then using the improved black kite algorithm to dynamically optimize the basis function of the fuzzy neural network, the network weight estimation update law, and the network reconstruction error upper bound estimation update law;

[0014] S3, using the matrix freedom formula and linear matrix inequality to solve the observer gain matrix and robust parameters, and then solving the observer gain matrix;

[0015] S4. Give the reachability inequality of the neural adaptive sliding mode observer;

[0016] S5. Based on the designed neural adaptive sliding mode observer, the execution describes the system state estimation and uncertainty estimation, completes the actuator and sensor concurrent fault estimation, satellite attitude angle estimation, and satellite attitude angular velocity estimation.

[0017] Preferably, in step S1, the model of the satellite attitude control system is:

[0018] ;

[0019] in, represent The derivative of , a time-varying scalar Represents time, , , They are: three-axis angle and three-axis angular velocity of the satellite, control input, and measurement output; , They are actuator failure and sensor failure respectively; , are external disturbance and measurement noise respectively; Victoria It is uncertain and has unknown nonlinear characteristics; , , , , , , , All are constant matrices: , They are , The coefficient matrix of for The measurement output matrix of , , , , They are , , , , The distribution matrix of; From the structure of the satellite attitude control system, we can know that , full rank; , are all full column rank matrices, and , represents the rank of the matrix;

[0020] Perform an equivalent transformation on the model of the satellite attitude control system, and let:

[0021] ;

[0022] Among them, the state transformation matrix And the output transformation matrix are all full-rank matrices, then the equivalent transformation system model of the satellite attitude control system is obtained:

[0023] ;

[0024] in, and are the state variables and measured output variables of the equivalent transformation system, respectively. for In Dimension variables, for The remaining sub-variables in for In Dimension variables, for The remaining sub-variables in ; , , , , , , , They are , , , , , , , The equivalent transformation matrix of , and satisfies:

[0025] , , , ,

[0026] , , , ;

[0027] in, , , , Represents matrices After block division, the 1×1th matrix block, the 1×2th matrix block, the 2×1th matrix block, and the 2×2th matrix block in the matrix; , Represents matrices After block division, the 1×1 matrix block and the 2×1 matrix block in the matrix; , Represents matrices After block division, the 1×1 matrix block and the 2×1 matrix block in the matrix; Representative Matrix After partitioning, the 1×1th matrix block in the matrix; and Representative Matrix After block division, the 1×1 matrix block and the 2×1 matrix block in the matrix; and Representative Matrix After block division, the 1×1 matrix block and the 2×2 matrix block in the matrix; Representative Matrix After blocking, the 2×1th matrix block in the matrix; Representative Matrix After the matrix is ​​divided into blocks, the 2×1th matrix block in the matrix; 0 represents that after each matrix is ​​divided into blocks, the elements in the matrix block are 0; according to the matrix transformation properties, , full rank; , Full rank, .

[0028] Preferably, in step S1, for the equivalent transformation system of the satellite attitude control system, let:

[0029] ;

[0030] in, is the reference output, the full rank matrix Actuator failure The reference output matrix of ;

[0031] make: , , , then we get the continuous-time uncertain description system:

[0032] ;

[0033] Among them, the singular matrix satisfy , represents a diagonal matrix, represents the identity matrix; and They represent the state variables and measurement outputs of the continuous-time uncertain description system respectively, and the other coefficient matrices are in the form of:

[0034] , , , , , , , ;

[0035] By performing a restricted equivalent transformation on the continuous-time uncertain description system, a continuous-time restricted equivalent uncertain description system is obtained:

[0036] ;

[0037] Among them, the restricted equivalent transformation matrix Not strange, is the state variable of the continuous-time constrained equivalent uncertain description system; at the same time, Expressed as , for In Dimension variables, for The remaining sub-variables in ;

[0038] The continuous-time restricted equivalent uncertain description system satisfies the strictly positive real condition:

[0039] .

[0040] Preferably, in step S2, for the continuous-time constrained equivalent uncertain description system, the fuzzy hyperbasis function neural network expression of its uncertainty is:

[0041] ;

[0042] Among them, the fuzzy hyperbasis function neural network is obtained by adding a fuzzy reasoning layer and a fuzzification layer to the hyperbasis function neural network; represents the basis functions of the fuzzy hyperbasis function neural network, represents the weights of the fuzzy hyperbasis function neural network, represents the network reconstruction error; , represent The modulus of, a positive scalar is the upper bound of the reconstruction error;

[0043] For the continuous-time constrained equivalent uncertain description system, a neural adaptive sliding mode observer is designed:

[0044] ;

[0045] in, is the intermediate variable, To describe the system state estimation term, used to estimate , In Dimension Variable To estimate , The remaining subvariables in To estimate ; is the uncertainty estimation term based on the improved fuzzy hyperbasis function neural network, which is used to estimate the uncertainty ; To improve the neural sliding mode estimation term, An improved sliding mode compensation term for network reconstruction error; , is the selected full rank matrix; and is the gain matrix to be designed.

[0046] Preferably, in step S2, the neural adaptive sliding mode observer is based on the uncertainty estimation term of the improved fuzzy hyperbasis function neural network. , design an improved neural sliding mode estimation term , Improved sliding mode compensation term for network reconstruction error :

[0047] ;

[0048] in, is the weight of the fuzzy hyperbasis function neural network An estimated value of To compensate for network reconstruction errors , Used to estimate the upper bound of the reconstruction error , represents the designed sliding surface, Represents the Signum function;

[0049] Defining Error Dynamics , represent The front Dimension error dynamics, represent The remaining sub-error dynamics in , then the designed sliding surface is:

[0050] ;

[0051] in, is a symmetric positive definite matrix.

[0052] Preferably, in step S2, the improved neural sliding mode estimation term and the improved sliding mode compensation term of the network reconstruction error are specifically improved by: using the improved circular chaos mapping method to improve the black kite algorithm, and then using the improved black kite algorithm to dynamically optimize the basis function of the fuzzy neural network, the network weight estimation update law and the network reconstruction error upper bound estimation update law, and the specific steps are:

[0053] S21. Generating the initial population: using the basis function of the fuzzy hyperbasis function neural network , adaptive parameters of the network weight estimation update law , the adaptive parameters of the update law for estimating the upper bound of the network reconstruction error Together they form the initial population of black-winged kites;

[0054] S22, executing the improved black-winged kite algorithm, specifically comprising the following steps:

[0055] S221, Black-winged kite population initialization:

[0056] For , , The initial population of black-winged kites is uniformly distributed by using the improved circular chaos mapping. The improved circular chaos mapping equation is:

[0057] ;

[0058] in, is the population at the previous moment, For the population at the next moment, Represents the remainder function, which is used to obtain the remainder of the division of two numbers;

[0059] Select the individual with the smallest fitness value as the leader of the black kite population, using the fitness function:

[0060] ;

[0061] in, is the fitness function;

[0062] S222, Black-winged Kite attack behavior:

[0063] ;

[0064] in, is the number of iterations currently completed; , Respectively A black kite Vidi The positions before and after the attack behavior are completed in the second iteration; is a constant, a random number ; , Represents natural numbers The index of is the total number of iterations given;

[0065] S223. Black-winged kite migration behavior:

[0066] ;

[0067] in, Indicates A black kite Dimension The position at the iteration, Indicates to The first iteration The leader of the Black Winged Kite; Indicates A black kite The first Dimension current position; Indicates In the iteration A black kite Fitness value of a random position in a dimension; random number ; represents the Cauchy variation, that is ; ;

[0068] S23. According to the final result of iterative optimization of the improved black-winged kite algorithm, the optimal basis function of the fuzzy hyperbasis function neural network is obtained. , Dynamic adaptive parameters of the network weight estimation update law , Dynamic adaptive parameters of the update law for estimating the upper bound of network reconstruction error ;

[0069] Among them, the calculation method of the network weight estimation update law and the network reconstruction error upper bound estimation update law is:

[0070] ;

[0071] in, represent The model, .

[0072] Preferably, in step S3, the observer gain matrix and robust parameters are solved using the matrix freedom formula and the linear matrix inequality, and the specific steps are:

[0073] S31. Use the following matrix freedom formula to solve the matrix to be designed. , , , :

[0074] ;

[0075] in, , represents pseudo-inverse;

[0076] S32, get , , , Then, use the following linear matrix inequality to solve the matrix to be designed , robust parameters , , :

[0077] ;

[0078] in, is a symmetric positive definite matrix, , , is a positive scalar;

[0079] S33, solve the observer gain matrix: use the obtained , , , , , the observer gain matrix is ​​calculated according to the following formula and :

[0080] ;

[0081] The observer gain matrix obtained by the above method is and Guaranteed error dynamics Asymptotically stable, and guaranteed For external disturbances , Actuator failure , sensor fault and measurement noise augmentation variables Robust, that is:

[0082] ;

[0083] in, , , , Respectively represent , , , The square of the 2-norm of .

[0084] Preferably, in step S4, the reachability of the neural adaptive sliding mode observer is guaranteed by the following inequality:

[0085] ;

[0086] in, , , , Respectively represent , , , Model; Represents the gain matrix Before After row partitioning, the 1×1 matrix block in the matrix; Represents the gain matrix Before The 1×2th matrix block in the matrix after row blocking; scalar .

[0087] Preferably, in step S5, the state estimation value of the system described in the continuous time constrained equivalent description system is calculated and uncertainty estimates ;

[0088] Depend on Calculate actuator fault estimate , sensor fault and measurement noise joint estimate , satellite attitude angle and attitude angular velocity estimates ;

[0089] Depend on Calculating sensor estimates .

[0090] Preferably, based on step S5, the estimation results of the designed observer are obtained, including a satellite attitude angle estimation curve, a satellite attitude angular velocity estimation curve, an actuator failure and sensor concurrent failure estimation curve, an uncertainty estimation curve, a fitness function iteration curve of a neural adaptive sliding mode observer based on an improved fuzzy hyperbasis function neural network, and indicator data for evaluating the estimation performance of the observer, wherein the indicator data is an absolute mean error.

[0091] Therefore, the present invention adopts the above-mentioned neural adaptive sliding mode observer design method for satellite attitude control system fault estimation, which has the following beneficial effects:

[0092] (1) The present invention fully considers the constraints such as concurrent actuator and sensor failures and uncertainties, external disturbances, and measurement noise, and performs an equivalent transformation on the attitude control system. The actuator failures, sensor failures, and measurement noise augmented variables are regarded as additional state variables of the satellite attitude control system, a continuous-time constrained equivalent uncertain description system is established, and a neural adaptive sliding mode observer for fault estimation is designed. This not only solves the problem of concurrent fault estimation of satellite attitude control systems under complex constraints, but also expands the application scope of the neural adaptive sliding mode observer in the description system.

[0093] (2) Aiming at the established continuous time constrained equivalent uncertain description system, the present invention adds a fuzzification layer and a fuzzy reasoning layer to the hyperbasis function neural network, and obtains a fuzzy hyperbasis function neural network (FHBFNN), thereby obtaining a better expression of uncertainty. Further, a neural adaptive sliding mode observer (IHBFNN-ASMO) based on an improved fuzzy hyperbasis function neural network is designed, including a description system state estimation term, an uncertainty estimation term based on an improved fuzzy hyperbasis function neural network; an improved neural sliding mode estimation term in the uncertainty estimation term and an improved sliding mode compensation term for network reconstruction error. The improvement method is as follows: the improved circular chaos mapping is used to improve the Black Kite Algorithm, and an improved Black Kite Algorithm (IBKA) with stronger ability to jump out of local optimality and faster convergence speed is obtained; the IBKA is used to dynamically optimize the basis function of the fuzzy neural network, the network weight estimation update law, and the network reconstruction error upper bound estimation update law, thereby further improving the neural network's ability to approximate uncertainty.

[0094] (3) The present invention utilizes the designed IHBFNN-ASMO based on IBKA (IBKA-IHBFNN-ASMO) to obtain better estimates of uncertainty and better estimates of actuator and sensor concurrent faults and satellite states (three-axis angles and three-axis angles). Compared with the previous neural adaptive sliding mode observer, higher estimation accuracy is obtained. At the same time, the designed IBKA-IHBFNN-ASMO ensures that the error dynamics obtain stronger robustness, thereby improving the overall performance of the fault estimation method.

[0095] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 It is a structural schematic diagram of an embodiment of a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation according to the present invention;

[0097] Figure 2 It is a roll angle estimation result diagram of a satellite attitude control system of an embodiment of a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation of the present invention;

[0098] Figure 3 It is a graph of the pitch angle estimation result of a satellite attitude control system of an embodiment of a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation of the present invention;

[0099] Figure 4 It is a diagram of the yaw angle estimation result of a satellite attitude control system of an embodiment of a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation of the present invention;

[0100] Figure 5 It is a rolling angular velocity estimation result diagram of a satellite attitude control system of an embodiment of a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation of the present invention;

[0101] Figure 6 It is a graph of the pitch angular velocity estimation result of a satellite attitude control system of an embodiment of a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation of the present invention;

[0102] Figure 7 It is a diagram of the yaw angular velocity estimation result of a satellite attitude control system of an embodiment of a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation of the present invention;

[0103] Figure 8 It is an actuator fault estimation result of an embodiment of a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation of the present invention;

[0104] Fig. 9 It is a sensor fault estimation result of an embodiment of a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation of the present invention;

[0105] Fig.10 The uncertainty estimation result is an embodiment of a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation of the present invention;

[0106] Fig.11 The present invention is a neural adaptive sliding mode observer design method for satellite attitude control system fault estimation, which is a comparison chart of adaptive function iteration results between IBKA-IFHBFNN-ASMO and BKA-FHBFNN-ASMO. DETAILED DESCRIPTION

[0107] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0108] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0109] The invention takes into account the constraints of concurrent actuator and sensor failures and uncertainties, external disturbances, measurement noise and the like of satellite ACSs, and performs equivalent transformation on the attitude control system; regards actuator failures, sensor failures and measurement noise augmented variables as additional state variables of ACSs, and establishes a continuous-time constrained equivalent uncertain description system; adds a fuzzification layer and a fuzzy reasoning layer to a hyperbasis function neural network (HBFNN) to obtain a fuzzy hyperbasis function neural network (FHBFNN); designs an adaptive sliding mode observer (IHBFNN-ASMO) based on an improved fuzzy hyperbasis function neural network, including designing a description system state estimation term and an uncertainty estimation term based on the improved fuzzy hyperbasis function neural network.

[0110] The improved neural sliding mode estimation term in the uncertainty estimation term and the improved sliding mode compensation term of the network reconstruction error are improved by introducing the improved circular chaos map to obtain the improved black kite algorithm (IBKA), and then using IBKA to dynamically optimize the basis function of the fuzzy neural network, the network weight estimation update law, and the network reconstruction error upper bound estimation update law to improve the neural network's approximation ability to nonlinear uncertainty. The observer gain matrix is ​​solved by linear matrix inequality, and the proposed neural adaptive sliding mode observer is used to achieve better uncertainty estimation, concurrent fault estimation, and satellite state (three-axis angle and angular velocity) estimation, which has important research significance.

[0111] like Figure 1As shown, a neural adaptive sliding mode observer design method for fault estimation of a satellite attitude control system includes the following steps:

[0112] S1. Considering concurrent actuator, sensor failure and uncertainty, external disturbance and measurement noise and other constraints, the satellite attitude control system is equivalently transformed; the actuator failure, sensor failure and measurement noise augmented variables are regarded as additional state variables of the satellite attitude control system, and a continuous time constrained equivalent uncertain description system is established;

[0113] The model of the satellite attitude control system of this embodiment is:

[0114] ;

[0115] in, represent The derivative of , a time-varying scalar Represents time, , , They are: the satellite's three-axis angle (i.e., roll angle, pitch angle, yaw angle) and three-axis angular velocity (i.e., roll angular velocity, pitch angular velocity, yaw angular velocity), control input, and measurement output; , They are actuator failure and sensor failure respectively; , are external disturbance and measurement noise respectively; Victoria It is uncertain and has unknown nonlinear characteristics; , , , , , , , All are constant matrices: , They are , The coefficient matrix of for The measurement output matrix of , , , , They are , , , , The distribution matrix of; From the structure of the satellite attitude control system, we can know that , full rank; , are all full column rank matrices, and , Represents the rank of the matrix.

[0116] Perform an equivalent transformation on the model of the satellite attitude control system, and let:

[0117] ;

[0118] Among them, the state transformation matrix And the output transformation matrix are all full-rank matrices, then the equivalent transformation system model of the satellite attitude control system is obtained:

[0119] ;

[0120] in, and are the state variables and measured output variables of the equivalent transformation system, respectively. for In Dimension variables, for The remaining sub-variables in for In Dimension variables, for The remaining sub-variables in ; , , , , , , , They are , , , , , , , The equivalent transformation matrix of , and satisfies:

[0121] , , , ,

[0122] , , , ;

[0123] in, , , , Represents matrices After block division, the 1×1th matrix block, the 1×2th matrix block, the 2×1th matrix block, and the 2×2th matrix block in the matrix; , Represents matrices After block division, the 1×1 matrix block and the 2×1 matrix block in the matrix; , Represents matrices After block division, the 1×1 matrix block and the 2×1 matrix block in the matrix; Representative Matrix After partitioning, the 1×1th matrix block in the matrix; and Representative Matrix After block division, the 1×1 matrix block and the 2×1 matrix block in the matrix; and Representative Matrix After block division, the 1×1 matrix block and the 2×2 matrix block in the matrix; Representative Matrix After blocking, the 2×1th matrix block in the matrix; Representative Matrix After the matrix is ​​divided into blocks, the 2×1th matrix block in the matrix; 0 represents that after each matrix is ​​divided into blocks, the elements in the matrix block are 0; according to the matrix transformation properties, , full rank; , Full rank, .

[0124] For the equivalent transformation system of the satellite attitude control system, let:

[0125] ;

[0126] in, is the reference output, the full rank matrix Actuator failure The reference output matrix of ;

[0127] make: , , , then we get the continuous-time uncertain description system:

[0128] ;

[0129] Among them, the singular matrix satisfy , represents a diagonal matrix, represents the identity matrix; and They represent the state variables and measurement outputs of the continuous-time uncertain description system respectively, and the other coefficient matrices are in the form of:

[0130] , , , , , , , ;

[0131] By performing a restricted equivalent transformation on the continuous-time uncertain description system, we can obtain the continuous-time restricted equivalent uncertain description system:

[0132] ;

[0133] Among them, the restricted equivalent transformation matrix Not strange, is the state variable of the continuous-time constrained equivalent uncertain description system. At the same time, It can be expressed as , for In Dimension variables, for The remaining sub-variables in .

[0134] Since the matrix , , Full rank, matrix , The columns are full of rank, , and the restricted equivalent transformation matrix Not strange, so , , From the matrix structure of , we can see that the continuous-time restricted equivalent uncertain description system satisfies the strict positive real condition:

[0135] .

[0136] S2. For the established restricted equivalent uncertain description system, a fuzzification layer and a fuzzy reasoning layer are added to the super basis function neural network to obtain a fuzzy super basis function neural network to obtain an uncertain fuzzy super basis function neural network expression;

[0137] Design a neural adaptive sliding mode observer with an estimation term describing the system state and an uncertainty estimation term based on an improved fuzzy hyperbasis function neural network;

[0138] Design an improved neural sliding mode estimation term in the uncertainty estimation term based on the improved fuzzy hyperbasis function neural network and an improved sliding mode compensation term for network reconstruction error;

[0139] The specific improvement methods of the improved neural sliding mode estimation term and the improved sliding mode compensation term of the network reconstruction error are: using the improved circular chaos mapping method to improve the Black Kite algorithm, and then using the improved Black Kite algorithm to dynamically optimize the basis function of the fuzzy neural network, the network weight estimation update law, and the network reconstruction error upper bound estimation update law.

[0140] For the continuous-time constrained equivalent uncertain description system, the fuzzy hyperbasis function neural network expression of its uncertainty is:

[0141] ;

[0142] Among them, the fuzzy hyperbasis function neural network is obtained by adding a fuzzy reasoning layer and a fuzzification layer to the hyperbasis function neural network; represents the basis functions of the fuzzy hyperbasis function neural network, represents the weights of the fuzzy hyperbasis function neural network, represents the network reconstruction error; , represent The modulus of, a positive scalar is the upper bound of the reconstruction error;

[0143] For the continuous-time constrained equivalent uncertain description system, the neural adaptive sliding mode observer structure is designed as follows:

[0144] ;

[0145] in, is the intermediate variable, To describe the system state estimation term, used to estimate , In Dimension Variable To estimate , The remaining subvariables in To estimate ; is the uncertainty estimation term based on the improved fuzzy hyperbasis function neural network, which is used to estimate the uncertainty ; To improve the neural sliding mode estimation term, An improved sliding mode compensation term for network reconstruction error; , is the selected full rank matrix; and is the gain matrix to be designed.

[0146] Neural adaptive sliding mode observer, for its uncertainty estimation term based on improved fuzzy hyperbasis function neural network , design an improved neural sliding mode estimation term , Improved sliding mode compensation term for network reconstruction error , has the following structure:

[0147] ;

[0148] in, is the weight of the fuzzy hyperbasis function neural network An estimated value of To compensate for network reconstruction errors , Used to estimate the upper bound of the reconstruction error , represents the designed sliding surface, Represents the Signum function.

[0149] Defining Error Dynamics , represent The front Dimension error dynamics, represent The remaining sub-error dynamics in , then the designed sliding surface is:

[0150] ;

[0151] in, is a symmetric positive definite matrix.

[0152] The specific improvement method of improving the neural sliding mode estimation term and the improved sliding mode compensation term of the network reconstruction error is: using the improved circular chaos mapping method to improve the black kite algorithm, and then using the improved black kite algorithm to dynamically optimize the basis function of the fuzzy neural network, the network weight estimation update law and the network reconstruction error upper bound estimation update law. The specific steps are:

[0153] S21. Generating the initial population: using the basis function of the fuzzy hyperbasis function neural network , adaptive parameters of the network weight estimation update law , the adaptive parameters of the update law for estimating the upper bound of the network reconstruction error Together they form the initial population of black-winged kites;

[0154] S22, executing the improved black-winged kite algorithm, specifically comprising the following steps:

[0155] S221, Black-winged kite population initialization:

[0156] For , , The initial population of black-winged kites is uniformly distributed by using the improved circular chaos mapping. The improved circular chaos mapping equation is:

[0157] ;

[0158] in, is the population at the previous moment, For the population at the next moment, Represents the remainder function, which is used to obtain the remainder of the division of two numbers;

[0159] Select the individual with the smallest fitness value as the leader of the black kite population, using the fitness function:

[0160] ;

[0161] in, is the fitness function;

[0162] S222, Black-winged Kite attack behavior:

[0163] ;

[0164] in, is the number of iterations currently completed; , Respectively A black kite Vidi The positions before and after the attack behavior are completed in the second iteration; is a constant, a random number ; , Represents natural numbers The index of is the total number of iterations given;

[0165] S223. Black-winged kite migration behavior:

[0166] ;

[0167] in, Indicates A black kite Dimension The position at the iteration, Indicates to The first iteration The leader of the Black Winged Kite; Indicates A black kite The first Dimension current position; Indicates In the iteration A black kite Fitness value of a random position in a dimension; random number ; represents the Cauchy variation, that is ; ;

[0168] S23. According to the final result of iterative optimization of the improved black-winged kite algorithm, the optimal basis function of the fuzzy hyperbasis function neural network is obtained. , Dynamic adaptive parameters of the network weight estimation update law , Dynamic adaptive parameters of the update law for estimating the upper bound of network reconstruction error ;

[0169] Among them, the calculation method of the network weight estimation update law and the network reconstruction error upper bound estimation update law is:

[0170] ;

[0171] in, represent The model, .

[0172] S3. Solve the observer gain matrix and robust parameters using the matrix freedom formula and linear matrix inequality, and then solve the observer gain matrix; it can ensure that the error dynamics are asymptotically stable, and can ensure the robustness of the error dynamics to external disturbances, actuator failures, sensor failures and measurement noise augmented variables;

[0173] Specifically, the observer gain matrix and robust parameters are solved using the matrix freedom formula and linear matrix inequality. The specific steps are as follows:

[0174] S31. Use the following matrix freedom formula to solve the matrix to be designed. , , , :

[0175] ;

[0176] in, , represents pseudo-inverse;

[0177] S32, get , , , Then, use the following linear matrix inequality to solve the matrix to be designed , robust parameters , , :

[0178] ;

[0179] in, is a symmetric positive definite matrix, , , is a positive scalar;

[0180] S33, solve the observer gain matrix: use the obtained , , , , , the observer gain matrix is ​​calculated according to the following formula and :

[0181] ;

[0182] The observer gain matrix obtained by the above method is and Guaranteed error dynamics Asymptotically stable, and guaranteed For external disturbances , Actuator failure , sensor fault and measurement noise augmentation variables Robust, that is:

[0183] ;

[0184] in, , , , Respectively represent , , , The square of the 2-norm of .

[0185] S4. The reachability inequality of the neural adaptive sliding mode observer is given to ensure the feasibility of the design scheme.

[0186] The reachability of the neural adaptive sliding mode observer is guaranteed by the following inequality:

[0187] ;

[0188] in, , , , Respectively represent , , , Model; Represents the gain matrix Before After row partitioning, the 1×1 matrix block in the matrix; Represents the gain matrix Before The 1×2th matrix block in the matrix after row blocking; scalar .

[0189] S5. Based on the designed neural adaptive sliding mode observer, the execution describes the system state estimation and uncertainty estimation, completes the actuator and sensor concurrent fault estimation, satellite attitude angle estimation, and satellite attitude angular velocity estimation.

[0190] Specifically, we calculate the state estimate of the system in the continuous-time constrained equivalent description system and uncertainty estimates ;

[0191] Depend on Calculate actuator fault estimate , sensor fault and measurement noise joint estimate , satellite attitude angle and attitude angular velocity estimates ;

[0192] Depend on Calculating sensor estimates .

[0193] The estimation results of the designed observer include satellite attitude angle estimation curve, satellite attitude angular velocity estimation curve, actuator fault and sensor concurrent fault estimation curve, uncertainty estimation curve, fitness function iteration curve of the neural adaptive sliding mode observer based on improved fuzzy hyperbasis function neural network, and indicator data for evaluating the estimation performance of the observer, wherein the indicator data is the absolute mean error.

[0194] In order to verify the performance of this implementation, three observers are used to estimate the faults of the target ACSs, and the estimation results of the three observers are compared. The three observers are: IBKA-IFHBFNN-ASMO, BKA-IFHBFNN-ASMO and FHBFNN-ASMO.

[0195] The test results are as follows Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Fig. 9 , Fig.10 as well as Fig.11 As shown, the neural adaptive observer based on this embodiment, namely, IBKA-IFHBFNN-ASMO, has a faster convergence speed, higher calculation accuracy and better ability to jump out of the global optimal solution, and has better robustness: the estimation results of the state (three-axis angle and three-axis angle) of the target ACSs, uncertainty, actuator and sensor concurrent faults are closest to the true values ​​of the corresponding variables of the target ACSs, and when there is an external disturbance in the system, the IBKA-IFHBFNN-ASMO estimation curve of this embodiment is smoother, which shows that the fault estimation method provided by the present invention has a more accurate estimation effect, can better suppress external disturbances, and obtains stronger robustness.

[0196] At the same time, Fig.11 As shown, the adaptive function iteration comparison diagram of BKA-IFHBFNN-ASMO and IBKA-IFHBFNN-ASMO of the present invention. The estimation accuracy is ensured by the more optimal adaptive function iteration method of IBKA during the estimation period.

[0197] Therefore, the present invention adopts the above-mentioned neural adaptive sliding mode observer design method for satellite attitude control system fault estimation, and obtains higher estimation accuracy compared with the previous neural adaptive sliding mode observer; at the same time, the designed IBKA-IHBFNN-ASMO ensures that the error dynamics obtains stronger robustness, thereby improving the overall performance of the fault estimation method.

[0198] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A neural adaptive sliding mode observer design method for satellite attitude control system fault estimation, characterized in that: The following steps are involved: S1. Consider concurrent actuator and sensor failures and uncertainties, external disturbances and measurement noise, and perform equivalent transformation on the satellite attitude control system; regard actuator failures, sensor failures and measurement noise augmented variables as additional state variables of the satellite attitude control system, and establish a continuous-time constrained equivalent uncertain description system; S2. For the established restricted equivalent uncertain description system, a fuzzification layer and a fuzzy reasoning layer are added to the super basis function neural network to obtain a fuzzy super basis function neural network to obtain an uncertain fuzzy super basis function neural network expression; Design a neural adaptive sliding mode observer with an estimation term describing the system state and an uncertainty estimation term based on an improved fuzzy hyperbasis function neural network; Design an improved neural sliding mode estimation term in the uncertainty estimation term based on the improved fuzzy hyperbasis function neural network and an improved sliding mode compensation term for network reconstruction error; Improved neural sliding mode estimation term and improved sliding mode compensation term of network reconstruction error. The specific improvement methods are: using the improved circular chaos mapping method to improve the black kite algorithm, and then using the improved black kite algorithm to dynamically optimize the basis function of the fuzzy neural network, the network weight estimation update law, and the network reconstruction error upper bound estimation update law; S3, using the matrix freedom formula and linear matrix inequality to solve the observer gain matrix and robust parameters, and then solving the observer gain matrix; S4. Give the reachability inequality of the neural adaptive sliding mode observer; S5. Based on the designed neural adaptive sliding mode observer, the execution describes the system state estimation and uncertainty estimation, completes the actuator and sensor concurrent fault estimation, satellite attitude angle estimation, and satellite attitude angular velocity estimation.

2. The method for designing a neural adaptive sliding mode observer for fault estimation of a satellite attitude control system according to claim 1, characterized in that: In step S1, the model of the satellite attitude control system is: ； in, represent The derivative of represents the three-axis angular velocity of the satellite, a time-varying scalar t Represents time, They are: three-axis angle of the satellite, control input, and measurement output; , They are actuator failure and sensor failure respectively; , are external disturbance and measurement noise respectively; Victoria It is uncertain and has unknown nonlinear characteristics; , , , , , , , All are constant matrices: , They are , The coefficient matrix of for The measurement output matrix of , , , , They are , , , , The distribution matrix of; From the structure of the satellite attitude control system, we can know that , full rank; , are all full column rank matrices, and , represents the rank of the matrix; Perform an equivalent transformation on the model of the satellite attitude control system, and let: ； Among them, the state transformation matrix And the output transformation matrix are all full-rank matrices, then the equivalent transformation system model of the satellite attitude control system is obtained: ； in, and are the state variables and measured output variables of the equivalent transformation system, respectively. for In Dimension variables, for The remaining sub-variables in for In Dimension variables, for The remaining sub-variables in ; , , , , , , , They are , , , , , , , The equivalent transformation matrix of , and satisfies: ， ， ， ， ， ， ， ； in, , , , Represents matrices After block division, the 1×1th matrix block, the 1×2th matrix block, the 2×1th matrix block, and the 2×2th matrix block in the matrix; , Represents matrices After block division, the 1×1 matrix block and the 2×1 matrix block in the matrix; , Represents matrices After block division, the 1×1 matrix block and the 2×1 matrix block in the matrix; Representative Matrix After partitioning, the 1×1th matrix block in the matrix; and Representative Matrix After block division, the 1×1 matrix block and the 2×1 matrix block in the matrix; and Representative Matrix After block division, the 1×1 matrix block and the 2×2 matrix block in the matrix; Representative Matrix After partitioning, the 2×1th matrix block in the matrix; Representative Matrix After the matrix is ​​divided into blocks, the 2×1th matrix block in the matrix; 0 represents that after each matrix is ​​divided into blocks, the elements in the matrix block are 0; according to the matrix transformation properties, , full rank; , Full rank, .

3. The neural adaptive sliding mode observer design method for fault estimation of a satellite attitude control system according to claim 2 is characterized in that: In step S1, for the equivalent transformation system of the satellite attitude control system, let: ； in, is the reference output, the full rank matrix Actuator failure The reference output matrix of ; make: , , , then we get the continuous-time uncertain description system: ； Among them, the singular matrix satisfy , represents a diagonal matrix, represents the identity matrix; and They represent the state variables and measurement outputs of the continuous-time uncertain description system respectively, and the other coefficient matrices are in the form of: ， ， ， ， ， ， ， ； By performing a restricted equivalent transformation on the continuous-time uncertain description system, a continuous-time restricted equivalent uncertain description system is obtained: ； Among them, the restricted equivalent transformation matrix Not strange, is the state variable of the continuous-time constrained equivalent uncertain description system; at the same time, Expressed as , for In Dimension variables, for The remaining sub-variables in ; The continuous-time restricted equivalent uncertain description system satisfies the strictly positive real condition: 。 4. The method for designing a neural adaptive sliding mode observer for fault estimation of a satellite attitude control system according to claim 3 is characterized in that: In step S2, for the continuous time constrained equivalent uncertain description system, the fuzzy hyperbasis function neural network expression of its uncertainty is: ； Among them, the fuzzy hyperbasis function neural network is obtained by adding a fuzzy reasoning layer and a fuzzification layer to the hyperbasis function neural network; represents the basis functions of the fuzzy hyperbasis function neural network, represents the weights of the fuzzy hyperbasis function neural network, represents the network reconstruction error; , represent The modulus of, a positive scalar is the upper bound of the reconstruction error; For the continuous-time constrained equivalent uncertain description system, a neural adaptive sliding mode observer is designed: ； in, is the intermediate variable, To describe the system state estimation term, used to estimate , In Dimension Variable To estimate , The remaining subvariables in To estimate ; is the uncertainty estimation term based on the improved fuzzy hyperbasis function neural network, which is used to estimate the uncertainty ; To improve the neural sliding mode estimation term, An improved sliding mode compensation term for network reconstruction error; , is the selected full rank matrix; and is the gain matrix to be designed.

5. The method for designing a neural adaptive sliding mode observer for fault estimation of a satellite attitude control system according to claim 4, characterized in that: In step S2, the neural adaptive sliding mode observer is based on the uncertainty estimation term of the improved fuzzy hyperbasis function neural network. , design an improved neural sliding mode estimation term , Improved sliding mode compensation term for network reconstruction error : ； in, is the weight of the fuzzy hyperbasis function neural network An estimated value of To compensate for network reconstruction errors , Used to estimate the upper bound of the reconstruction error , represents the designed sliding surface, Represents the Signum function; Defining Error Dynamics , represent The front Dimension error dynamics, represent The remaining sub-error dynamics in , then the designed sliding surface is: ； in, is a symmetric positive definite matrix.

6. The method for designing a neural adaptive sliding mode observer for fault estimation of a satellite attitude control system according to claim 5, characterized in that: In step S2, the improved neural sliding mode estimation term and the improved sliding mode compensation term of the network reconstruction error are specifically improved by using the improved circular chaos mapping method to improve the black kite algorithm, and then using the improved black kite algorithm to dynamically optimize the basis function of the fuzzy neural network, the network weight estimation update law and the network reconstruction error upper bound estimation update law, and the specific steps are: S21. Generating the initial population: using the basis function of the fuzzy hyperbasis function neural network , adaptive parameters of the network weight estimation update law , the adaptive parameters of the update law for estimating the upper bound of the network reconstruction error Together they form the initial population of black-winged kites; S22, executing the improved black-winged kite algorithm, specifically comprising the following steps: S221, Black-winged kite population initialization: For , , The initial population of black-winged kites is uniformly distributed by using the improved circular chaos mapping. The improved circular chaos mapping equation is: ； in, is the population at the previous moment, For the population at the next moment, Represents the remainder function, which is used to obtain the remainder of the division of two numbers; Select the individual with the smallest fitness value as the leader of the black kite population, using the fitness function: ； in, is the fitness function; S222, Black-winged Kite attack behavior: ； in, is the number of iterations currently completed; , Respectively A black kite Vidi The positions before and after the attack behavior are completed in the second iteration; is a constant, a random number ; , Represents natural numbers The index of is the total number of iterations given; S223. Black-winged kite migration behavior: ； in, Indicates A black kite Dimension The position at the iteration, Indicates to The first iteration The leader of the Black Winged Kite; Indicates A black kite The first Dimension current position; Indicates In the iteration A black kite Fitness value of a random position in a dimension; random number ; represents the Cauchy variation, that is ; ; S23. According to the final result of iterative optimization of the improved black-winged kite algorithm, the optimal basis function of the fuzzy hyperbasis function neural network is obtained. , Dynamic adaptive parameters of the network weight estimation update law , Dynamic adaptive parameters of the update law for estimating the upper bound of network reconstruction error ; Among them, the calculation method of the network weight estimation update law and the network reconstruction error upper bound estimation update law is: ； in, represent The model, .

7. The method for designing a neural adaptive sliding mode observer for fault estimation of a satellite attitude control system according to claim 6, characterized in that: In step S3, the observer gain matrix and robust parameters are solved using the matrix freedom formula and linear matrix inequality. The specific steps are: S31. Use the following matrix freedom formula to solve the matrix to be designed. , , , : ； in, , represents pseudo-inverse; S32, get , , , Then, use the following linear matrix inequality to solve the matrix to be designed , robust parameters , , : ； in, is a symmetric positive definite matrix, , , is a positive scalar; S33, solve the observer gain matrix: use the obtained , , , , , the observer gain matrix is ​​calculated according to the following formula and : ； The observer gain matrix obtained by the above method is and Guaranteed error dynamics Asymptotically stable, and guaranteed For external disturbances , Actuator failure , sensor fault and measurement noise augmentation variables Robust, that is: ； in, , , , Respectively represent , , , The square of the 2-norm of .

8. The method for designing a neural adaptive sliding mode observer for fault estimation of a satellite attitude control system according to claim 7, characterized in that: In step S4, the reachability of the neural adaptive sliding mode observer is guaranteed by the following inequality: ； in, , , , Respectively represent , , , Model; Represents the gain matrix Before After row partitioning, the 1×1 matrix block in the matrix; Represents the gain matrix Before The 1×2th matrix block in the matrix after row blocking; scalar .

9. The method for designing a neural adaptive sliding mode observer for fault estimation of a satellite attitude control system according to claim 8, characterized in that: In step S5, the state estimation value of the system described in the continuous time constrained equivalent description system is calculated. and uncertainty estimates ; Depend on Calculate actuator fault estimate , sensor fault and measurement noise joint estimate , satellite attitude angle and attitude angular velocity estimates ; Depend on Calculating sensor estimates .

10. The method for designing a neural adaptive sliding mode observer for fault estimation of a satellite attitude control system according to claim 9, characterized in that: Based on step S5, the estimation results of the designed observer are obtained, including a satellite attitude angle estimation curve, a satellite attitude angular velocity estimation curve, an actuator fault and a sensor concurrent fault estimation curve, an uncertainty estimation curve, a fitness function iteration curve of a neural adaptive sliding mode observer based on an improved fuzzy hyperbasis function neural network, and indicator data for evaluating the estimation performance of the observer, wherein the indicator data is an absolute mean error.

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