Non-linear non-strict feedback multi-agent system fixed time fault-tolerant control system

Abstract

The invention discloses a non-linear non-strict feedback multi-agent system fixed time fault-tolerant control system, and belongs to the technical field of agent system cooperative control. Comprising a multi-agent system model, a coordinate transformation and command filtering module, an error compensation signal module, a backstepping recursion module, a neural network module, an adaptive law module and an adaptive fault-tolerant controller module. The method is used for compensating the influence of sensor faults on system consistency and ensuring that the system converges within fixed time, so that when the system has sensor deviation, gain and other faults, the system can still realize output consistent tracking within a predetermined time upper limit irrelevant to an initial state, the reliability and safety of the system are remarkably improved, and the system reliability and safety are improved. The technical problems of state feedback information distortion and system cooperation precision and stability reduction caused by sensor faults of the intelligent agent in the prior art are solved.

Description

Technical Field

[0001] This application belongs to the field of cooperative control technology for nonlinear multi-agent systems (MASs), specifically relating to a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system. Background Technology

[0002] With the widespread application of multi-agent systems in fields such as UAV swarms, intelligent transportation, and distributed sensor networks, the issues of system reliability and security are becoming increasingly prominent. In actual operation, agent sensors are prone to malfunctions such as deviations and gain changes due to environmental interference, aging, or hardware damage, leading to distorted state feedback information and severely affecting the collaborative accuracy and stability of the system. Existing technologies face the following challenges in addressing these issues:

[0003] First, traditional fault-tolerant control methods mostly focus on actuator failures, with relatively insufficient research on sensor failures. Sensor failures directly disrupt the state feedback loop, and in multi-agent systems, fault information spreads through communication networks, leading to an overall degradation of cooperative performance. Existing methods often assume a single or known fault mode, making it difficult to adapt to time-varying and complex sensor failures.

[0004] Second, most existing control strategies are based on strict feedback system architectures, making them difficult to directly extend to non-strict feedback systems. In non-strict feedback structures, the nonlinear terms of each subsystem are coupled with each other, making it difficult to decouple them step by step during controller design, which increases the complexity of system analysis and the difficulty of controller design.

[0005] Third, while finite-time control methods can achieve fast convergence, their convergence time depends on the initial state of the system. In practical applications, it is often difficult to obtain accurate initial information in advance, which limits their practicality. In addition, traditional designs based on backstepping require repeated differentiation of the virtual control law, which can easily lead to "computational explosion" and "singularity" problems, restricting the real-time performance and engineering feasibility of the algorithm. Summary of the Invention

[0006] Purpose of the invention: This application develops a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system, aiming to solve the technical problems in the prior art of distortion of state feedback information caused by sensor failures of agents and decrease in the accuracy and stability of system coordination.

[0007] Technical Solution: This application provides a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system, applicable to a nonlinear, non-strict feedback multi-agent system comprising multiple agents, including:

[0008] A multi-agent system model is used to receive the outputs of the agents and output state information;

[0009] The coordinate transformation and command filtering module is used to receive the status information and output a virtual control signal and an output signal generated by the virtual control signal through a filter.

[0010] An error compensation signal module is used to receive the virtual control signal and the output signal, and output an error compensation signal;

[0011] The backstepping recursion module is used to receive the error compensation signal and output a signal reflecting the rate of change of system stability;

[0012] A neural network module is used to receive the state information and output the corrected error variable;

[0013] The adaptive law module is used to receive the state information, the output of the agent, the corrected error variable, and the signal reflecting the rate of change of system stability, and output the parameter adaptive law in combination with the ideal weight values ​​of the radial basis neural network.

[0014] An adaptive fault-tolerant controller module is used to receive the parameter adaptive law and the signal reflecting the rate of change of system stability, and to obtain the output of the intelligent agent.

[0015] In some embodiments, the representation formula of the multi-agent system model includes:

[0016] ;

[0017] ;

[0018] ;

[0019] in, Let h be the first derivative of the h-th state variable of the i-th agent in a multi-agent system; The (h+1)th state variable of the i-th agent in a multi-agent system; Let be the state vector of the i-th agent in a multi-agent system; Let h be an unknown smooth nonlinear function of the h-th state variable of the i-th agent in a multi-agent system; For time; For the external disturbance to the h-th state variable of the i-th agent in a multi-agent system; Let be the first derivative of the nth state variable of the i-th agent in a multi-agent system; This represents the output of the i-th agent in a multi-agent system. Let n be an unknown smooth nonlinear function of the nth state variable of the i-th agent in a multi-agent system. For the external disturbance to the nth state variable of the i-th agent in a multi-agent system; This is the input for the i-th agent in a multi-agent system; Let be the first state variable of the i-th agent in a multi-agent system. The sensor has a bias gain fault.

[0020] In some embodiments, the characterization formula for the deviation gain fault includes:

[0021] ;

[0022] in, For the sensor fault parameters of the i-th agent in a multi-agent system; Let be the first state variable of the i-th agent in a multi-agent system; Let be the unknown smooth perturbation of the i-th agent in a multi-agent system.

[0023] In some embodiments, the representation formula of the coordinate transformation and command filtering module includes:

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] in, Let be the dimension of the system state. , ; For the index of the agent in a nonlinear, non-strict feedback agent system model; For tracking error; Let be the set of neighboring agents of the i-th agent in a multi-agent system; The i-th agent is the th agent in the set of neighboring agents. One intelligent agent; These are the adjacency matrix elements of the communication topology; This is the input for the i-th agent; For the neighboring agents of the i-th agent Input; Let be the connection weight between the i-th agent and the leader; Signals to leaders; For the i-th agent, the first... One error variable; In a multi-agent system, the i-th agent is the... One state variable; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal; For design parameters; For the i-th agent, the first... Correction values ​​for each error variable; For the i-th agent, the first... One error variable; For the i-th agent, the first... Error compensation signals for each error variable.

[0030] In some embodiments, the characterization formula of the error compensation signal module includes:

[0031] ;

[0032] ;

[0033] ;

[0034] ;

[0035] in, For the i-th agent, the first... Compensation signals for each error variable, , For the number of error variables, 2 to The number between; , These are the adjacency matrix elements of the communication topology. Let i be the set of neighboring agents of the i-th agent in a multi-agent system. The i-th agent is the th agent in the set of neighboring agents. An intelligent agent. Let be the connection weight between the i-th agent and the leader; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal; For the p-th error variable of the i-th agent, there are positive design parameters; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal.

[0036] In some embodiments, the characterization formula of the backstepping recursion module includes:

[0037] ;

[0038] in, A signal reflecting the rate of change in system stability; The number of intelligent agents; For the index of the agent in a nonlinear, non-strict feedback agent system model; The number of error variables; This is the sort number of the error variable; Positive design parameters; Let k be the error variable of the i-th agent; Positive design parameters; Positive design parameters; Positive design parameters; To estimate the error; Positive design parameters; Positive design parameters; Let n be the error variable of the i-th agent; This represents the output of the i-th agent in a multi-agent system. Let n be an unknown smooth nonlinear function of the nth state variable of the i-th agent in a multi-agent system. Let be the state vector of the i-th agent in a multi-agent system; For the i-th agent, the first... Compensation signals for each error variable; For the i-th agent, the first... Compensation signals for each error variable; For the nth error variable of the i-th agent, the positive design parameters are: For the i-th agent, the first... The first derivative of the output signal generated by the step virtual control signal through the command filter; For the external disturbance to the nth state variable of the i-th agent in a multi-agent system; For time; Let n be the (n-1)th error variable of the i-th agent; Positive design parameters; Positive design parameters; To estimate the error, , For adaptive parameters The estimated value; Positive design parameters; , For the (n-1)th error variable of the i-th agent, (This refers to the positive design parameters.) It is a constant; Positive design parameters; To estimate the error, For adaptive parameters The estimated value.

[0039] In some embodiments, the representation formula of the neural network module includes:

[0040] ;

[0041] ;

[0042] ;

[0043] in, For the index of the agent in a nonlinear, non-strict feedback agent system model; Let be the dimension of the system state. , It is a nonlinear dynamic function; The corrected error variable; External interference; For sensor fault parameters; State variables The first derivative; For smooth disturbances; Let be the set of neighboring agents of the i-th agent in a multi-agent system; The i-th agent is the th agent in the set of neighboring agents. One intelligent agent; These are the adjacency matrix elements of the communication topology; These are the ideal weights for a radial basis function neural network. are basis functions; It is a smooth nonlinear function; To approximate the error; For compensation signals; This is the state vector.

[0044] In some embodiments, the characterization formula of the adaptive law module includes:

[0045] ;

[0046] ;

[0047] in, Let be the dimension of the system state. ; For the index of agents in a nonlinear, non-strict feedback agent system model; and For parameter adaptive law; for The estimate, , These are the ideal weights for a radial basis function neural network. for The estimate, , These are the ideal weights for a radial basis function neural network. , , , , , , , and Positive design parameters; The corrected error variable; , , and These are basis functions.

[0048] In some embodiments, the characterization formula of the adaptive fault-tolerant controller module includes:

[0049] ;

[0050] in, This represents the output of the i-th agent in a multi-agent system. For the i-th agent, the first... One error variable; For the i-th agent, the first... One error variable; Positive design parameters; The corrected error variable; for The estimate, , These are the ideal weights for a radial basis function neural network. , are basis functions; For the i-th agent, the first... Step virtual control signal; Positive design parameters; Positive design parameters; Positive design parameters; The design parameters are positive.

[0051] Beneficial Effects: Compared with the prior art, the embodiments of this application provide a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system, including a multi-agent system model, a coordinate transformation and command filtering module, an error compensation signal module, a backstepping recursion module, a neural network module, an adaptive law module, and an adaptive fault-tolerant controller module. The multi-agent system model is used to receive the outputs of the agents and output state information. The coordinate transformation and command filtering module is used to receive state information and output virtual control signals and output signals generated by filtering the virtual control signals. The error compensation signal module is used to receive virtual control signals and output signals, and output error compensation signals. The backstepping recursion module is used to receive error compensation signals and output signals reflecting the rate of change of system stability. The neural network module is used to receive state information and output corrected error variables. The adaptive law module is used to receive state information, agent outputs, corrected error variables, and signals reflecting the rate of change of system stability, and outputs parameter adaptive laws by combining the ideal weight values ​​of the radial basis function neural network. The adaptive fault-tolerant controller module is used to receive parameter adaptive laws and signals reflecting the rate of change of system stability, and obtain the outputs of the agents. This application constructs an error compensation signal by using the signal output from the coordinate transformation and command filtering module to compensate for the impact of sensor failure on system consistency, ensuring that the system converges within a fixed time. This enables the system to achieve consistent output tracking within a predetermined time limit, independent of the initial state, even when sensor deviations, gain failures, or other faults occur. This significantly improves the reliability and security of the system and solves the technical problems of distorted state feedback information and decreased system coordination accuracy and stability caused by sensor failures in existing technologies. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a schematic diagram of the structure of a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system provided in an embodiment of this application.

[0054] Figure 2This is a schematic diagram of the communication topology in a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system provided in an embodiment of this application.

[0055] Figure 3 Tracking error trajectory diagram of a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system provided in this application embodiment;

[0056] Figure 4 A comparison trajectory diagram of the outputs of the follower and the leader in a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system provided in this application embodiment;

[0057] Figure 5 The control input signal in the fixed-time fault-tolerant control system of the nonlinear, non-strict feedback multi-agent system provided in the embodiments of this application. Trajectory graph;

[0058] Figure 6 A module connection diagram of a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system provided in an embodiment of this application;

[0059] Figure reference numerals: 10, Multi-agent system model; 20, Coordinate transformation and command filtering module; 30, Error compensation signal module; 40, Backstepping recursion module; 50, Neural network module; 60, Adaptive law module; 70, Adaptive fault-tolerant controller module. Detailed Implementation

[0060] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0061] With the widespread application of multi-agent systems in fields such as UAV swarms, intelligent transportation, and distributed sensor networks, the issues of system reliability and security are becoming increasingly prominent. In actual operation, agent sensors are prone to malfunctions such as deviations and gain changes due to environmental interference, aging, or hardware damage, leading to distorted state feedback information and severely affecting the collaborative accuracy and stability of the system. Existing technologies face the following challenges in addressing these issues:

[0062] First, traditional fault-tolerant control methods mostly focus on actuator failures, with relatively insufficient research on sensor failures. Sensor failures directly disrupt the state feedback loop, and in multi-agent systems, fault information spreads through communication networks, leading to an overall degradation of cooperative performance. Existing methods often assume a single or known fault mode, making it difficult to adapt to time-varying and complex sensor failures.

[0063] Second, most existing control strategies are based on strict feedback system architectures, making them difficult to directly extend to non-strict feedback systems. In non-strict feedback structures, the nonlinear terms of each subsystem are coupled with each other, making it difficult to decouple them step by step during controller design, which increases the complexity of system analysis and the difficulty of controller design.

[0064] Third, while finite-time control methods can achieve fast convergence, their convergence time depends on the initial state of the system. In practical applications, it is often difficult to obtain accurate initial information in advance, which limits their practicality. In addition, traditional designs based on backstepping require repeated differentiation of the virtual control law, which can easily lead to "computational explosion" and "singularity" problems, restricting the real-time performance and engineering feasibility of the algorithm.

[0065] In view of this, embodiments of this application provide a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system. Please refer to [link to relevant documentation]. Figure 1 and Figure 6 , Figure 1 This is a schematic diagram of the structure of a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system provided in an embodiment of this application. Figure 6This is a module connection diagram of a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system provided in this application embodiment. The nonlinear, non-strict feedback multi-agent system fixed-time fault-tolerant control system provided in this application embodiment includes a multi-agent system model 10, a coordinate transformation and command filtering module 20, an error compensation signal module 30, a backstepping recursion module 40, a neural network module 50, an adaptive law module 60, and an adaptive fault-tolerant controller module 70. The multi-agent system model 10 is used to receive the outputs of the agents and output state information; the coordinate transformation and command filtering module 20 is used to receive state information and output virtual control signals, and the virtual control signals are filtered to produce... The system comprises the following modules: an output signal; an error compensation signal module 30 receives the virtual control signal and the output signal, and outputs the error compensation signal; a backstepping recursion module 40 receives the error compensation signal and outputs a signal reflecting the rate of change of system stability; a neural network module 50 receives state information and outputs the corrected error variable; an adaptive law module 60 receives state information, the agent's output, the corrected error variable, and the signal reflecting the rate of change of system stability, and outputs the parameter adaptive law in combination with the ideal weight values ​​of the radial basis neural network; and an adaptive fault-tolerant controller module 70 receives the parameter adaptive law and the signal reflecting the rate of change of system stability, and obtains the agent's output. This application constructs an error compensation signal using the signal output by the coordinate transformation and command filtering module 20. This signal is used to compensate for the impact of sensor failures on system consistency, ensuring that the system converges within a fixed time. Even when sensor deviations, gain errors, or other faults occur, the system can still achieve consistent output tracking within a predetermined time bound independent of the initial state, significantly improving the system's reliability and safety. This solves the technical problems in the prior art where sensor failures cause distortion of the agent's state feedback information and a decrease in system coordination accuracy and stability.

[0066] In some embodiments, a nonlinear, non-strict feedback multi-agent system model 10 is constructed, including sensor fault terms. and disturbance terms , The characterization formula for the nonlinear, non-rigid feedback multi-agent system model 10 includes Formula 1:

[0067] ;

[0068] ;

[0069] ;

[0070] in, Let h be the first derivative of the h-th state variable of the i-th agent in a multi-agent system. ; The (h+1)th state variable of the i-th agent in a multi-agent system; Let be the state vector of the i-th agent in a multi-agent system. , This refers to the index of the agent in a nonlinear, non-strict feedback agent system model. , The total number of intelligent agents. It is a real number; Let h be an unknown smooth nonlinear function of the h-th state variable of the i-th agent in a multi-agent system; For time; For the external disturbance to the h-th state variable of the i-th agent in a multi-agent system, , for The upper bound; Let be the first derivative of the nth state variable of the i-th agent in a multi-agent system; This represents the output of the i-th agent in a multi-agent system. Let n be an unknown smooth nonlinear function of the nth state variable of the i-th agent in a multi-agent system. For an external disturbance to the nth state variable of the i-th agent in a multi-agent system, , for The upper bound; This is the input for the i-th agent in a multi-agent system; Let be the first state variable of the i-th agent in a multi-agent system. The sensor's bias gain fault, , These are the sensor fault parameters for the i-th agent in a multi-agent system. Let be the first state variable of the i-th agent in a multi-agent system; For the unknown smooth perturbation of the i-th agent in a multi-agent system, , ,satisfy , .

[0071] In some embodiments, this application designs a coordinate transformation and command filtering module 20, which introduces command filtering technology to process virtual control signals, avoiding the "computational explosion" and "singularity" problems in the traditional backstepping method. The representation formula of the coordinate transformation and command filtering module 20 includes Formula 2:

[0072] ;

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] in, Let be the dimension of the system state. , ; For the index of the agent in a nonlinear, non-strict feedback agent system model; For tracking error; Let be the set of neighboring agents of the i-th agent in a multi-agent system; The i-th agent is the th agent in the set of neighboring agents. One intelligent agent; These are the adjacency matrix elements of the communication topology; This is the input for the i-th agent; For the neighboring agents of the i-th agent Input; Let be the connection weight between the i-th agent and the leader; Signals to leaders; For the i-th agent, the first... One error variable, ; In a multi-agent system, the i-th agent is the... One state variable; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal; For design parameters; For the i-th agent, the first... Correction values ​​for each error variable, This is used to isolate the effects of faults and simplify controller design; For the i-th agent, the first... One error variable; For the i-th agent, the first... Error compensation signals for each error variable.

[0078] In some embodiments, this application constructs an error compensation signal based on the signal output by the coordinate transformation and command filtering module 20 to compensate for the impact of sensor failure on system consistency and ensure that the system converges within a fixed time. The characterization formula of the error compensation signal module 30 includes:

[0079] ;(Formula 3)

[0080] ;(Formula 4)

[0081] ;(Formula 5)

[0082] ;(Formula 6)

[0083] in, For the i-th agent, the first... Compensation signals for each error variable, , For the number of error variables, 2 to The number between , representing the initial value of the compensation signal for the error variable; , These are the adjacency matrix elements of the communication topology. Let i be the set of neighboring agents of the i-th agent in a multi-agent system. The i-th agent is the th agent in the set of neighboring agents. An intelligent agent. Let be the connection weight between the i-th agent and the leader; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal; For the p-th error variable of the i-th agent, there are positive design parameters; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal.

[0084] In some embodiments, this application designs a virtual controller and an adaptive fault-tolerant controller step by step based on backstepping recursion technology, combines radial basis function neural networks to approximate unknown nonlinear functions in the system, and introduces a fixed-time convergence term to ensure that the system tracking error converges to the neighborhood of the equilibrium point within a fixed time. The steps obtained by the backstepping recursion module 40 include:

[0085] Step 1: Calculate the error variable derivative Formula 7:

[0086] ;

[0087] Constructing Lyapunov functions This is represented by Formula 8:

[0088] ;

[0089] in, These are design parameters. , To estimate the error, , For adaptive parameters, , They are respectively , The estimated value, Indicates the error variable. Let represent the first unknown smooth nonlinear function of the i-th agent in the system. Let represent the first unknown smooth nonlinear function of the j-th agent in the system. This represents the second state variable in the state vector of the j-th agent;

[0090] ;

[0091] ;

[0092] in, and These are the ideal weights for a radial basis function neural network.

[0093] Based on Equation 7 and Young's inequality, Equation 8 can be rewritten as Equation 9:

[0094] ;

[0095] Step 2: Calculate the error variables derivative For formula 10:

[0096] ;

[0097] The Lyapunov function is constructed as shown in Formula 11:

[0098] ;

[0099] in, These are design parameters. To estimate the error, For adaptive parameters, yes The estimated value, , These are the ideal weights for a radial basis function neural network.

[0100] According to Equation 10 and Young's inequality, Equation 11 can be rewritten as Equation 12:

[0101] ;

[0102] in, , , , , , , , , , and These are positive design parameters. and It is an unknown constant.

[0103] No. ( Step 1: Calculate the error variable derivative Formula 13 as follows:

[0104] ;

[0105] The Lyapunov function is constructed as shown in Formula 14:

[0106]

[0107] in, These are design parameters. To estimate the error, For adaptive parameters, yes The estimated value, , These are the ideal weights for a radial basis function neural network.

[0108] Similar to formula 12, formula 14 can be rewritten as formula 15:

[0109] ;

[0110] in, , , , , and These are positive design parameters. It is an unknown constant.

[0111] No. Step: Calculate the error variable derivative Formula 16:

[0112] ;

[0113] The Lyapunov function is constructed as Equation 17:

[0114] ;

[0115] in, These are design parameters. To estimate the error, For adaptive parameters, yes The estimated value, , These are the ideal weights for a radial basis function neural network.

[0116] Similar to formula 15, formula 17 can be rewritten as formula 18:

[0117] ;

[0118] in, A signal reflecting the rate of change in system stability; The number of intelligent agents; For the index of the agent in a nonlinear, non-strict feedback agent system model; The number of error variables; This is the sort number of the error variable; Positive design parameters; Let k be the error variable of the i-th agent; Positive design parameters; Positive design parameters; Positive design parameters; To estimate the error; Positive design parameters; Positive design parameters; Let n be the error variable of the i-th agent; This represents the output of the i-th agent in a multi-agent system. Let n be an unknown smooth nonlinear function of the nth state variable of the i-th agent in a multi-agent system. Let be the state vector of the i-th agent in a multi-agent system; For the i-th agent, the first... Compensation signals for each error variable; For the i-th agent, the first... Compensation signals for each error variable; For the nth error variable of the i-th agent, the positive design parameters are: For the i-th agent, the first... The first derivative of the output signal generated by the step virtual control signal through the command filter; For the external disturbance to the nth state variable of the i-th agent in a multi-agent system; For time; Let n be the (n-1)th error variable of the i-th agent; Positive design parameters; Positive design parameters; To estimate the error, , For adaptive parameters The estimated value; Positive design parameters; , For the (n-1)th error variable of the i-th agent, (This refers to the positive design parameters.) It is an unknown constant; Positive design parameters; To estimate the error, For adaptive parameters The estimated value.

[0119] In some embodiments, the neural network module 50 utilizes information such as state information in the multi-agent system, and uses adaptive parameters and neural network radial basis functions to approximate the unknown nonlinear dynamics, then sends it to the adaptive law module 60 for further processing. Due to the nonlinear dynamics... , Completely unknown, the neural network module 50 is used for processing and it is assumed that the representation formula of the neural network module 50 includes:

[0120] ;(Formula 19)

[0121] ;(Formula 20)

[0122] ;(Formula 21)

[0123] in, For the index of the agent in a nonlinear, non-strict feedback agent system model; Let be the dimension of the system state. , It is a nonlinear dynamic function; The corrected error variable. ; External interference; For sensor fault parameters; State variables The first derivative; For smooth disturbances; Let be the set of neighboring agents of the i-th agent in a multi-agent system; The i-th agent is the th agent in the set of neighboring agents. One intelligent agent; These are the adjacency matrix elements of the communication topology; These are the ideal weights for a radial basis function neural network. are basis functions; It is a smooth nonlinear function; To approximate the error, , , , , and It is an unknown constant; For compensation signals; This is the state vector.

[0124] Understandably, this application is applicable to nonlinear multi-agent systems with non-strict feedback structures. By combining radial basis neural networks to approximate unknown dynamics and incorporating an adaptive compensation mechanism, it can effectively suppress the impact of sensor failures on cooperative performance while ensuring that all closed-loop signals are consistent and bounded, thereby enhancing the robustness and adaptability of the system.

[0125] In some embodiments, the input to the adaptive law module 60 is the state information of the multi-agent system and the output of the backstepping recursion technique module. The output signals are respectively , Its function is to reflect the dynamic changes of adaptive parameters in the controller, and then input the dynamic changes of parameters into the adaptive fault-tolerant controller module 70 to achieve adaptive compensation for sensor faults. The characterization formula of the adaptive law module includes:

[0126] ;(Formula 22)

[0127] ;(Formula 23)

[0128] in, Let be the dimension of the system state. ; For the index of agents in a nonlinear, non-strict feedback agent system model; and For parameter adaptive law; for The estimate, , These are the ideal weights for a radial basis function neural network. for The estimate, , These are the ideal weights for a radial basis function neural network. , , , , , , , and Positive design parameters; The corrected error variable; , , and As basis functions, , , , .

[0129] In some embodiments, the input to the adaptive fault-tolerant controller module 70 is the output of the backstepping recursion module 40. Output of Adaptive Law Module 60 , This ensures that, in the event of sensor failure, the multi-agent system output maintains consistent tracking within a fixed timeframe, and that all closed-loop signals are bounded. The characterization formula for the adaptive fault-tolerant controller module 70 includes:

[0130] ;

[0131] in, This represents the output of the i-th agent in a multi-agent system. For the i-th agent, the first... One error variable; For the i-th agent, the first... One error variable; Positive design parameters; The corrected error variable; for The estimate, , For the i-th agent, the first... Ideal weights for a radial basis function neural network with error variables; , As basis functions, ; For the i-th agent, the first... Step virtual control signal; Positive design parameters; Positive design parameters; Positive design parameters; These are positive design parameters.

[0132] Understandably, this application addresses common sensor faults in multi-agent systems by designing an adaptive fault-tolerant controller with fixed-time convergence characteristics. This enables the system to maintain consistent output tracking within a predetermined time bound independent of the initial state even when sensor bias or gain faults occur, significantly improving the system's reliability and security.

[0133] Understandably, the nonlinear, non-strict feedback multi-agent system fixed-time fault-tolerant control system provided in this application includes a multi-agent system model 10, a coordinate transformation and command filtering module 20, an error compensation signal module 30, a backstepping recursion module 40, a neural network module 50, an adaptive law module 60, and an adaptive fault-tolerant controller module 70. The multi-agent system model 10 is used to receive the output of the agents and output state information. The coordinate transformation and command filtering module 20 is used to receive state information and output virtual control signals and output signals generated by filtering the virtual control signals. The error compensation signal module 30 is used to receive virtual control signals and output signals, and output error compensation signals. The backstepping recursion module 40 is used to receive error compensation signals and output signals reflecting the rate of change of system stability. The neural network module 50 is used to receive state information and output corrected error variables. The adaptive law module 60 is used to receive state information, agent outputs, corrected error variables, and signals reflecting the rate of change of system stability, and outputs parameter adaptive laws by combining the ideal weight values ​​of the radial basis function neural network. The adaptive fault-tolerant controller module 70 is used to receive parameter adaptive laws and signals reflecting the rate of change of system stability, and obtain the output of the agents. This application constructs an error compensation signal by using the coordinate transformation and the signal output by the command filtering module 20 to compensate for the impact of sensor failure on system consistency, ensuring that the system converges within a fixed time. This enables the system to achieve consistent output tracking within a predetermined time limit, independent of the initial state, even when sensor deviations, gain failures, or other faults occur. This significantly improves the reliability and safety of the system and solves the technical problems of distorted state feedback information and decreased system coordination accuracy and stability caused by sensor failures in existing technologies.

[0134] For example, the communication topology selected for the simulation is as follows: Figure 2 As shown, Figure 2 This diagram illustrates the communication topology in a fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system, as provided in an embodiment of this application. The topology consists of one leader and four follower agents. Simulation results are as follows... Figures 3 to 5 As shown, this indicates that all signals within a multi-agent system remain bounded. Figure 3 The tracking error trajectory diagram of the fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system provided in this application embodiment is given by... Figure 3 It can be seen that the system synchronization error of the first agent... The system synchronization error of the second agent The system synchronization error of the third agent All fluctuate within a very small range; Figure 4 The output trajectory comparison diagram of the follower and leader in the fixed-time fault-tolerant control system of the nonlinear, non-strict feedback multi-agent system provided in the embodiments of this application is from... Figure 4 As can be seen, all followers can track the leader's signal with high precision, and there is no overshoot or oscillation. Figure 5 The control input signal in the fixed-time fault-tolerant control system of the nonlinear, non-strict feedback multi-agent system provided in the embodiments of this application. trajectory map, by Figure 5 It can be seen that the input signal generated by the controller when suppressing faults and disturbances is smooth and bounded, which conforms to the physical limits of the actual actuator.

[0135] This application has provided a detailed description of a nonlinear, non-strict feedback multi-agent system fixed-time fault-tolerant control system provided in the embodiments of this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system, characterized in that, Applied to nonlinear, non-strict feedback multi-agent systems involving multiple agents, including: A multi-agent system model (10) is used to receive the outputs of the agents and output state information; The coordinate transformation and command filtering module (20) is used to receive the status information and output the virtual control signal and the output signal generated by the virtual control signal through the filter; An error compensation signal module (30) is used to receive the virtual control signal and the output signal, and output an error compensation signal; The backstepping recursion module (40) is used to receive the error compensation signal and output a signal reflecting the rate of change of system stability; The neural network module (50) is used to receive the state information and output the corrected error variable; The adaptive law module (60) is used to receive the state information, the output of the agent, the corrected error variable and the signal reflecting the rate of change of system stability, and output the parameter adaptive law in combination with the ideal weight value of the radial basis neural network. An adaptive fault-tolerant controller module (70) is used to receive the adaptive law of parameters and the signal reflecting the rate of change of system stability, and to obtain the output of the intelligent agent.

2. The fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system according to claim 1, characterized in that, The characterization formula of the multi-agent system model (10) includes: ； ； ； in, Let h be the first derivative of the h-th state variable of the i-th agent in a multi-agent system; The (h+1)th state variable of the i-th agent in a multi-agent system; Let be the state vector of the i-th agent in a multi-agent system; Let h be an unknown smooth nonlinear function of the h-th state variable of the i-th agent in a multi-agent system; For time; For the external disturbance to the h-th state variable of the i-th agent in a multi-agent system; Let be the first derivative of the nth state variable of the i-th agent in a multi-agent system; This represents the output of the i-th agent in a multi-agent system. Let n be an unknown smooth nonlinear function of the nth state variable of the i-th agent in a multi-agent system. For the external disturbance to the nth state variable of the i-th agent in a multi-agent system; This is the input for the i-th agent in a multi-agent system; Let be the first state variable of the i-th agent in a multi-agent system. The sensor has a bias gain fault.

3. The fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system according to claim 2, characterized in that, The characterization formula for the deviation gain fault includes: ； in, For the sensor fault parameters of the i-th agent in a multi-agent system; Let be the first state variable of the i-th agent in a multi-agent system; Let be the unknown smooth perturbation of the i-th agent in a multi-agent system.

4. The fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system according to claim 1, characterized in that, The representation formulas of the coordinate transformation and command filtering module (20) include: ； ； ； ； ； in, Let be the dimension of the system state. , ; For the index of the agent in a nonlinear, non-strict feedback agent system model; For tracking error; Let be the set of neighboring agents of the i-th agent in a multi-agent system; The i-th agent is the th agent in the set of neighboring agents. One intelligent agent; These are the adjacency matrix elements of the communication topology; This is the input for the i-th agent; For the neighboring agents of the i-th agent Input; Let be the connection weight between the i-th agent and the leader; Signals to leaders; For the i-th agent, the first... One error variable; In a multi-agent system, the i-th agent is the... One state variable; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal; For design parameters; For the i-th agent, the first... Correction values ​​for each error variable; For the i-th agent, the first... One error variable; For the i-th agent, the first... Error compensation signals for each error variable.

5. The fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system according to claim 1, characterized in that, The characterization formula of the error compensation signal module (30) includes: ； ； ； ； in, For the i-th agent, the first... Compensation signals for each error variable, , For the number of error variables, 2 to The number between; , These are the adjacency matrix elements of the communication topology. Let i be the set of neighboring agents of the i-th agent in a multi-agent system. The i-th agent is the th agent in the set of neighboring agents. An intelligent agent. Let be the connection weight between the i-th agent and the leader; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal; For the p-th error variable of the i-th agent, there are positive design parameters; For the i-th agent, the first... The output signal generated by the step virtual control signal through the command filter; For the i-th agent, the first... Step virtual control signal.

6. The fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system according to claim 1, characterized in that, The characterization formula of the backstep recursion module (40) includes: ; in, A signal reflecting the rate of change in system stability; The number of intelligent agents; For the index of the agent in a nonlinear, non-strict feedback agent system model; The number of error variables; This is the sort number of the error variable; Positive design parameters; Let k be the error variable of the i-th agent; Positive design parameters; Positive design parameters; Positive design parameters; To estimate the error; Positive design parameters; Positive design parameters; Let n be the error variable of the i-th agent; This represents the output of the i-th agent in a multi-agent system. Let n be an unknown smooth nonlinear function of the nth state variable of the i-th agent in a multi-agent system. Let be the state vector of the i-th agent in a multi-agent system; For the i-th agent, the first... Compensation signals for each error variable; For the i-th agent, the first... Compensation signals for each error variable; For the nth error variable of the i-th agent, the positive design parameters are: For the i-th agent, the first... The first derivative of the output signal generated by the step virtual control signal through the command filter; For the external disturbance to the nth state variable of the i-th agent in a multi-agent system; For time; Let n be the (n-1)th error variable of the i-th agent; Positive design parameters; Positive design parameters; To estimate the error, , For adaptive parameters The estimated value; Positive design parameters; , For the (n-1)th error variable of the i-th agent, (This refers to the positive design parameters.) It is a constant; Positive design parameters; To estimate the error, For adaptive parameters The estimated value.

7. The fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system according to claim 1, characterized in that, The representation formula of the neural network module (50) includes: ； ； ； in, For the index of the agent in a nonlinear, non-strict feedback agent system model; Let be the dimension of the system state. , It is a nonlinear dynamic function; The corrected error variable; External interference; For sensor fault parameters; State variables The first derivative; For smooth disturbances; Let be the set of neighboring agents of the i-th agent in a multi-agent system; The i-th agent is the th agent in the set of neighboring agents. One intelligent agent; These are the adjacency matrix elements of the communication topology; These are the ideal weights for a radial basis function neural network. are basis functions; It is a smooth nonlinear function; To approximate the error; For compensation signals; This is the state vector.

8. The fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system according to claim 1, characterized in that... The characterization formula of the adaptive law module (60) includes: ； ； in, Let be the dimension of the system state. ; For the index of agents in a nonlinear, non-strict feedback agent system model; and For parameter adaptive law; for The estimate, , These are the ideal weights for a radial basis function neural network. for The estimate, , These are the ideal weights for a radial basis function neural network. , , , , , , , and Positive design parameters; The corrected error variable; , , and These are basis functions.

9. The fixed-time fault-tolerant control system for a nonlinear, non-strict feedback multi-agent system according to claim 1, characterized in that... The characterization formula of the adaptive fault-tolerant controller module (70) includes: ； in, This represents the output of the i-th agent in a multi-agent system. For the i-th agent, the first... One error variable; For the i-th agent, the first... One error variable; Positive design parameters; The corrected error variable; for The estimate, , These are the ideal weights for a radial basis function neural network. , are basis functions; For the i-th agent, the first... Step virtual control signal; Positive design parameters; Positive design parameters; Positive design parameters; The design parameters are positive.

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