Nonlinear multi-agent system fixed time consensus control method and device and medium

Abstract

The present application relates to the field of artificial intelligence and control technology, in particular to a nonlinear multi-agent system fixed-time consensus control method, device and medium. The control method takes the backstepping recursive method as the control design framework, proposes an adaptive fixed-time consensus controller based on an auxiliary compensation system, and solves the nonlinear multi-agent system consensus control problem under time-varying input delay. By providing and changing the control input signal by a person, the multi-agent system motion trajectory can be modified according to the demand. The time-varying input delay and unknown nonlinear function are considered in the system model, making the system more general. Among them, the unknown time-varying delay function is processed by constructing an auxiliary compensation system, and the unknown nonlinear function is processed by using a radial basis function neural network approximation. According to the fixed-time control related lemma, a practical fixed-time adaptive consensus control method is proposed to ensure that the consensus error of the multi-agent system converges to the neighborhood of the origin within a fixed time.

Description

Technical Field

[0001] This invention relates to the fields of artificial intelligence and control technology, and in particular to a fixed-time consistency control method, device and medium for nonlinear multi-agent systems. Background Technology

[0002] Consistent control of multi-agent systems is the core foundation for realizing applications such as unmanned swarm collaboration (e.g., drone formations, robot cooperation) and smart grid synchronization. Its goal is to design distributed control laws that enable a group of intelligent agents that rely solely on local neighborhood information interaction to achieve asymptotic or precise convergence of their states (position, velocity, attitude, etc.) within a finite time.

[0003] However, real-world multi-agent systems face severe challenges, such as inherent strong nonlinear dynamics, pervasive model uncertainty, unavoidable communication / input delays, and complex external disturbances. Traditional consensus protocols based on ideal linear models and graph theory are insufficient to effectively address these combined uncertainties, nonlinearities, and time-delay coupling effects. There is an urgent need to integrate advanced control strategies to construct robust, efficient solutions with stringent performance guarantees. Summary of the Invention

[0004] The main objective of this invention is to provide a fixed-time consistency control method, device, and medium for nonlinear multi-agent systems, which aims to address the combined uncertainties, nonlinearity, and time-delay coupling effects.

[0005] To achieve the above objectives, the first aspect of this invention provides a fixed-time consistency control method for a nonlinear multi-agent system, applied to a nonlinear multi-agent system with time-varying input delay. The nonlinear multi-agent system includes one dynamic leader system with control signals provided by a human and N follower systems, comprising the following steps:

[0006] S1: Establish a dynamic model and a network communication topology model for a multi-agent system. The dynamic model incorporates an unknown time-varying delay function and a nonlinear function.

[0007] S2: Construct an auxiliary compensation system of the same order as the multi-autonomous system to process unknown time-varying delay functions, and construct a radial basis function neural network to approximate and process unknown nonlinear functions;

[0008] S3: Based on the actual fixed-time stability theory, an adaptive fixed-time consistency controller based on an auxiliary compensation system is constructed using the backstepping method; a nonlinear filter is introduced to estimate the virtual control signal.

[0009] S4: Verify the stability of the adaptive fixed-time consistency controller based on Lyapunov and fixed-time stability theory.

[0010] Further, optionally, the dynamic model includes a follower system model and a leader system model;

[0011] The follower system model is as follows:

[0012] ;

[0013] in, , ; Represents the system state vector; Indicates the first The first agent of the intelligent agent The derivative of the first-order state; Indicates the first The first agent of the intelligent agent The derivative of the first-order state; Indicates the first The first agent of the intelligent agent Unknown order smooth nonlinear function; Indicates the first The first agent of the intelligent agent The derivative of the first-order state; Indicates a term with delay. The system input signal; Indicates the first The first agent of the intelligent agent Unknown order smooth nonlinear function; Indicates the first The system output signal of each intelligent agent; Indicates the first The first-order system state signal of each agent;

[0014] The leader system model is as follows:

[0015] ;

[0016] in, The derivative of the leader system state signal; This represents a continuous and bounded control input signal; Indicates the leader system status signal; Indicates the input parameters of the leader system; This indicates the output signal of the leader system.

[0017] Further, optionally, the leader system is marked as 0, and the follower system is marked as... ;

[0018] Network communication topology model express, For inclusion A directed graph with n nodes, where Represents a set of nodes. Represents the set of edges; Representing the self To the self Transmitting information; nodes Represents a node Adjacent nodes;

[0019] make Represent the adjacency matrix, when hour, ;when hour, ; node The set of adjacent nodes is ;

[0020] definition For the first The in-degree matrix of each autonomous entity, where ;

[0021] Define the Laplace matrix as The root node is defined as the leader node. ;

[0022] When the subject When obtaining leader information, define Assume that at least one self-entity possesses a directed path to every other node, i.e., a directed graph. It has a spanning tree.

[0023] Further optionally, the auxiliary compensation system is:

[0024] ;

[0025] in, , Indicates the first The derivative of the first-order auxiliary compensation signal of each agent; ; Indicates the first The second-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Represents a symbolic function; Indicates the first The first-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Indicates the first The derivative of the second-order auxiliary compensation signal of the agent; Indicates the first The third-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; Indicates the first The first intelligent agent The derivative of the first-order auxiliary compensation signal; Indicates the first The first agent of the intelligent agent Auxiliary compensation signal; Indicates a design parameter that is greater than zero; Indicates the first The first agent of the intelligent agent Auxiliary compensation signal; Indicates a design parameter that is greater than zero; Indicates the first The first agent of the intelligent agent Auxiliary compensation signal; Indicates the first The derivative of the nth-order auxiliary compensation signal of an agent; This represents the difference between the control input and the control output. ; Indicates the control input signal; Indicates a design parameter that is greater than zero; Indicates the first The nth-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Indicates the first The first agent of the intelligent agent Auxiliary compensation signal; This indicates a design parameter that is greater than zero.

[0026] Alternatively, the radial basis function neural network is:

[0027] definition To be compact A continuous function on the following radial basis function neural network. It can be used to approximate functions : ;in, This represents the ideal weight vector with o being the number of elements in the neural network; Let be the input vector, and This represents the input dimension of the neural network; Indicates network reconstruction error. Represents a constant greater than zero; Represents a basis function vector;

[0028] Define the optimal weight vector as:

[0029] ;

[0030] Design a Gaussian function for:

[0031] , ;

[0032] in, Indicates the center of the receiving field. This represents the width of the Gaussian function.

[0033] Further, optionally, constructing an adaptive fixed-time consistency controller based on an auxiliary compensation system includes the following steps:

[0034] Step S31: Define the consistency error of a multi-agent system as:

[0035] ;

[0036] in, and ; Indicates the first The output signal of each intelligent agent; This indicates the output signal of the leader system; Indicates the first The output signal of each intelligent agent; Indicates the first The connection coefficient between each agent and the leader;

[0037] The coordinate transformation design is as follows:

[0038] ;

[0039] in, Indicates based on Compensated consistency error Indicates virtual error. ; Indicates the filtered output signal. Indicates virtual control signal, This represents the filtering error signal in a nonlinear filter; Indicates the first The first agent of the intelligent agent System state;

[0040] After differentiating the consistency error signal, the following nonlinear function is constructed:

[0041] ;

[0042] , ;

[0043] ;

[0044] Represents the integrated nonlinear function. Indicates the first The first-order nonlinear function of an agent Indicates the first The second-order system state of an agent, Indicates the first The first-order nonlinear function of an agent express Design parameters, This indicates a design parameter that is greater than zero. Represents the integrated nonlinear function. Indicates the first The first agent of the intelligent agent Order-order nonlinear function, This indicates a design parameter that is greater than zero. Represents the integrated nonlinear function. Indicates the first The nth-order nonlinear function of an agent Indicates a design parameter that is greater than zero;

[0045] Using radial basis function neural networks to approximate nonlinear functions , and ,Right now:

[0046] ;

[0047] in, , Represents the integrated state vector. , ;

[0048] Step S32: Construct a nonlinear filter and filter parameter update law As shown below:

[0049] ;

[0050] in, and Indicates the filter parameters; Indicate the design parameters, satisfying ,and and All are natural numbers; express The estimated value, express The upper realm, Indicates the first The first intelligent agent The absolute value of the derivative of the first-order virtual control signal; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; express The initial value of the estimate;

[0051] Step S33: Design the virtual control signals for steps 1 to n-1 by selecting the appropriate Lyapunov function. and adaptive fixed-time consistency controller As shown below:

[0052] ;

[0053] in, This represents the virtual control signal for step 1; Indicates a design parameter that is greater than zero; express; express The estimated value, , This represents the ideal weighted state value; , representing the integrated state vector; Indicates the first The first-order system state of each agent;

[0054] ;

[0055] in, =2,…,n-1; Indicates the first Virtual control signals for each step; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; express The estimated value, , This represents the ideal weighted state value; Represents the integrated state vector, and ;

[0056] ;

[0057] in, ,and , ; Indicates a design parameter that is greater than zero; Indicates a virtual error signal; This indicates the filtering error signal; Indicates filter design parameters that are greater than zero; Indicates filter design parameters that are greater than zero; Indicates a design parameter that is greater than zero; Represents the integrated state vector. ,and ; express The estimated value, express The upper realm, This represents the derivative of the virtual control signal at step n; express The estimated value, , This represents the ideal weighted state value;

[0058] Design the adaptive law for steps 1 through n. As shown below:

[0059] ;

[0060] in, , and All are design parameters; This indicates a design parameter that is greater than zero.

[0061] Further, optionally, verifying the stability of the adaptive fixed-time consensus controller includes the following steps:

[0062] Step S41: Select the Lyapunov function from step 1 to step n as:

[0063] ;

[0064] , ;

[0065] ;

[0066] in, , , , All of these represent design parameters that are greater than zero; The Lyapunov function for step 1; Indicates the first Lyapunov function of the step, Denotes the Lyapunov function at step n;

[0067] Step S42: Differentiate the selected Lyapunov function, process it using Young's inequality scaling technique, substitute the virtual control signal and adaptive law, and finally transform the Lyapunov function. The derivative, when rearranged, yields:

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] in, , Represents the set of minimum constant parameters. Represents the Lyapunov function V Power of 1 Represents the set of minimum constant parameters. Represents the Lyapunov function V Power of 1 Represents the known functions of integration. Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, express The upper realm, Indicates the first Virtual control signals for steps, This represents the known function integrated in step n;

[0073] Step S43: Combining mathematical expectation and fixed-time stability theory, we can obtain The expected value and convergence time of the square are as follows:

[0074] ;

[0075] ;

[0076] , , ;

[0077] in, This represents the consistency error (when r=1) or the virtual error signal. Indicates the error convergence time. This represents the maximum error convergence time. Indicates design parameters, Representing Lyapunov functions The expected value.

[0078] A second aspect of the present invention discloses a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in the first aspect of the present invention.

[0079] A second aspect of the present invention discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in the first aspect of the present invention.

[0080] The technical solution provided by this invention may include the following beneficial effects:

[0081] Based on practical fixed-time control theory, this invention proposes an adaptive fixed-time consistency control method to ensure that the consistency error of a multi-agent system converges to the neighborhood of the origin within a fixed time, effectively improving the transient performance of the closed-loop system, and the convergence time does not depend on the initial state of the system.

[0082] Specifically, by constructing an auxiliary compensation system of the same order as the multi-agent system, an auxiliary signal is generated to compensate for the unknown time-varying delay function, effectively solving the delay problem and improving the system robustness. This method is suitable for cooperative control of nonlinear multi-agent systems. Furthermore, this invention estimates the virtual control signal by constructing a nonlinear filter, obtaining its estimated value for control design. This avoids repeatedly differentiating the signal, effectively reducing the complexity of derivation and calculation in control design.

[0083] It is worth noting that in this invention, the consistency control reference trajectory is generated by the leader through human decision signals, rather than a traditional reference signal, which offers better practicality. Known leader input signals are incorporated into the control design to obtain corresponding control commands. Simultaneously, when the leader's control input signals are unknown, they can be approximated using neural networks. Attached Figure Description

[0084] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0085] Figure 1This is a flowchart of the fixed-time consistency control method for nonlinear multi-agent systems according to the present invention;

[0086] Figure 2 This is a directed communication topology diagram between a leader entity and multiple follower entities according to an embodiment of the present invention;

[0087] Figure 3 This is a diagram illustrating the overall control framework of a controlled system according to an embodiment of the present invention.

[0088] Figure 4 This is a diagram illustrating the overall consistency control effect of a multi-agent system according to an embodiment of the present invention, including the output signals of all follower agents. and the output signals of the leader's self ;

[0089] Figure 5 This is a consistency error signal according to an embodiment of the present invention. Simulation results;

[0090] Figure 6 The filtering error signal is an embodiment of the present invention. Simulation results;

[0091] Figure 7 This is a system control input signal according to an embodiment of the present invention. Simulation results. Detailed Implementation

[0092] The technical solutions of the embodiments of the present invention 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 the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0093] The following is combined Figure 1 This invention describes a fixed-time consistency control method for nonlinear multi-agent systems disclosed in its first aspect, applicable to nonlinear multi-agent systems with time-varying input delays, such as unmanned swarm collaboration (e.g., drone formation, robot cooperation) and smart grid synchronization. The nonlinear multi-agent system includes one dynamic leader system with control signals provided by a human and N follower systems.

[0094] The control method includes the following steps:

[0095] S1: Establish a dynamic model of the multi-agent system and a network communication topology model. The dynamic model incorporates unknown time-varying delay functions and nonlinear functions. The network communication topology model is based on directed graph theory and constructed by combining the information interaction relationships between multiple agents.

[0096] S2: Construct an auxiliary compensation system of the same order as the multi-autonomous system to process the unknown time-varying delay function, and construct a radial basis function neural network to approximate and process the unknown nonlinear function. In this embodiment, by constructing an auxiliary system to compensate (process) the input delay signal, a virtual time-delay-free dynamic model is constructed to actively cancel the time delay effect, transforming the original system into an equivalent "time-delay-free" closed loop.

[0097] S3: Based on the actual fixed-time stability theory, an adaptive fixed-time consistent controller based on an auxiliary compensation system is constructed using the backstepping method. A nonlinear filter is introduced to estimate the virtual control signal. The actual fixed-time control, through the introduction of a dynamic compensation mechanism, ensures that the system can stabilize within a finite time acceptable to engineering applications, even under real-world conditions such as parameter uncertainties, external disturbances, and input constraints, with the convergence time independent of the initial state. This application simultaneously integrates actual fixed-time control and a nonlinear filter into the traditional backstepping recursive control framework. The nonlinear filter completely eliminates the high-order differential explosion problem of the virtual control law, avoiding the dependence of the traditional backstepping method on analytical derivatives. Simultaneously, relying on the fixed-time convergence mechanism, the upper bound and accuracy of the system tracking error convergence time are strictly preset (independent of the initial state), significantly improving robustness to sudden disturbances and parameter perturbations. Ultimately, this achieves a unified control objective of high precision, fast response, and strong disturbance rejection in a strongly nonlinear system.

[0098] S4: Verifying the stability of the adaptive fixed-time consistency controller based on Lyapunov and fixed-time stability theory. This embodiment constructs a quadratic Lyapunov function, primarily to prove the boundedness of error signals in the closed-loop system, such as formation error, virtual error, filtering error, and neural network approximation error, based on Lyapunov stability theory, i.e., to prove the system stability.

[0099] Based on practical fixed-time control theory, this invention proposes an adaptive fixed-time consistency control method to ensure that the consistency error of a multi-agent system converges to the neighborhood of the origin within a fixed time, effectively improving the transient performance of the closed-loop system, and the convergence time does not depend on the initial state of the system.

[0100] Specifically, by constructing an auxiliary compensation system of the same order as the multi-agent system, an auxiliary signal is generated to compensate for the unknown time-varying delay function, effectively solving the delay problem and improving the system robustness. This method is suitable for cooperative control of nonlinear multi-agent systems. Furthermore, this invention estimates the virtual control signal by constructing a nonlinear filter, obtaining its estimated value for control design. This avoids repeatedly differentiating the signal, effectively reducing the complexity of derivation and calculation in control design.

[0101] It is worth noting that in this invention, the consistency control reference trajectory is generated by the leader through human decision signals, rather than a traditional reference signal, which offers better practicality. Known leader input signals are incorporated into the control design to obtain corresponding control commands. Simultaneously, when the leader's control input signals are unknown, they can be approximated using neural networks.

[0102] As an optional implementation, in step S1, a general dynamic model of a nonlinear multi-agent system is established, which includes a follower system model and a leader system model:

[0103] The follower system model is as follows:

[0104] ;

[0105] in, , ; Represents the system state vector; Indicates the first The first agent of the intelligent agent The derivative of the first-order state; Indicates the first The first agent of the intelligent agent The derivative of the first-order state; Indicates the first The first agent of the intelligent agent Unknown order smooth nonlinear function; Indicates the first The first agent of the intelligent agent The derivative of the first-order state; Indicates a term with delay. The system input signal; Indicates the first The first agent of the intelligent agent Unknown order smooth nonlinear function; Indicates the first The system output signal of each intelligent agent; Indicates the first The first-order system state signal of each agent;

[0106] The leader system model is as follows:

[0107] ;

[0108] in, The derivative of the leader system state signal; This represents a continuous and bounded control input signal; Indicates the leader system status signal; Indicates the input parameters of the leader system; This indicates the output signal of the leader system.

[0109] Specifically, optionally, the leader system is marked as 0, and the follower system is marked as... Network communication topology model express, For inclusion A directed graph with n nodes, where Represents a set of nodes. Represents the set of edges; Representing the self To the self Transmitting information; nodes Represents a node Adjacent nodes; let Represent the adjacency matrix, when hour, ;when hour, ; node The set of adjacent nodes is ;definition For the first The in-degree matrix of each autonomous entity, where Define the Laplace matrix as The root node is defined as the leader node. When the subject When obtaining leader information, define Assume that at least one self-entity possesses a directed path to every other node, i.e., a directed graph. It has a spanning tree.

[0110] For example, the auxiliary compensation system is:

[0111] ;

[0112] in, , Indicates the first The derivative of the first-order auxiliary compensation signal of each agent; ; Indicates the first The second-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Represents a symbolic function; Indicates the first The first-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Indicates the first The derivative of the second-order auxiliary compensation signal of the agent; Indicates the first The third-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; Indicates the first The first intelligent agent The derivative of the first-order auxiliary compensation signal; Indicates the first The first agent of the intelligent agent Auxiliary compensation signal; Indicates a design parameter that is greater than zero; Indicates the first The first agent of the intelligent agent Auxiliary compensation signal; Indicates a design parameter that is greater than zero; Indicates the first The first agent of the intelligent agent Auxiliary compensation signal; Indicates the first The derivative of the nth-order auxiliary compensation signal of an agent; This represents the difference between the control input and the control output. ; Indicates the control input signal; Indicates a design parameter that is greater than zero; Indicates the first The nth-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Indicates the first The first agent of the intelligent agent Auxiliary compensation signal; This indicates a design parameter that is greater than zero.

[0113] For example, a radial basis function neural network is as follows:

[0114] definition To be compact A continuous function on the following radial basis function neural network. It can be used to approximate functions : ;in, This represents the ideal weight vector with o being the number of elements in the neural network; Let be the input vector, and This represents the input dimension of the neural network; Indicates network reconstruction error. Represents a constant greater than zero; Represents a basis function vector;

[0115] Define the optimal weight vector as:

[0116] ;

[0117] Design a Gaussian function for:

[0118] , ;

[0119] in, Indicates the center of the receiving field. This represents the width of the Gaussian function.

[0120] In step S3, constructing an adaptive fixed-time consistency controller based on an auxiliary compensation system includes the following steps:

[0121] Step S31: Define the consistency error of a multi-agent system as:

[0122] ;

[0123] in, and ; Indicates the first The output signal of each intelligent agent; This indicates the output signal of the leader system; Indicates the first The output signal of each intelligent agent; Indicates the first The connection coefficient between each agent and the leader;

[0124] The coordinate transformation design is as follows:

[0125] ;

[0126] in, Indicates based on Compensated consistency error Indicates virtual error. ; Indicates the filtered output signal. Indicates virtual control signal, This represents the filtering error signal in a nonlinear filter; Indicates the first The first agent of the intelligent agent System state;

[0127] After differentiating the consistency error signal, the following nonlinear function is constructed:

[0128] ;

[0129] , ;

[0130] ;

[0131] Represents the integrated nonlinear function. Indicates the first The first-order nonlinear function of an agent Indicates the first The second-order system state of an agent, Indicates the first The first-order nonlinear function of an agent express Design parameters, This indicates a design parameter that is greater than zero. Represents the integrated nonlinear function. Indicates the first The first agent of the intelligent agent Order-order nonlinear function, This indicates a design parameter that is greater than zero. Represents the integrated nonlinear function. Indicates the first The nth-order nonlinear function of an agent Indicates a design parameter that is greater than zero;

[0132] Using radial basis function neural networks to approximate nonlinear functions , and ,Right now:

[0133] ;

[0134] in, , Represents the integrated state vector. , ;

[0135] Step S32: Construct a nonlinear filter and filter parameter update law As shown below:

[0136] ;

[0137] in, and Indicates the filter parameters; Indicate the design parameters, satisfying ,and and All are natural numbers; express The estimated value, express The upper realm, Indicates the first The first intelligent agent The absolute value of the derivative of the first-order virtual control signal; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; express The initial value of the estimate;

[0138] Step S33: Design the virtual control signals for steps 1 to n-1 by selecting the appropriate Lyapunov function. and adaptive fixed-time consistency controller As shown below:

[0139] ;

[0140] in, This represents the virtual control signal for step 1; Indicates a design parameter that is greater than zero; express; express The estimated value, , This represents the ideal weighted state value; , representing the integrated state vector; Indicates the first The first-order system state of each agent;

[0141] ;

[0142] in, =2,…,n-1; Indicates the first Virtual control signals for each step; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; express The estimated value, , This represents the ideal weighted state value; Represents the integrated state vector, and ;

[0143] ;

[0144] in, ,and , ; Indicates a design parameter that is greater than zero; Indicates a virtual error signal; This indicates the filtering error signal; Indicates filter design parameters that are greater than zero; Indicates filter design parameters that are greater than zero; Indicates a design parameter that is greater than zero; Represents the integrated state vector. ,and ; express The estimated value, express The upper realm, This represents the derivative of the virtual control signal at step n; express The estimated value, , This represents the ideal weighted state value;

[0145] Design the adaptive law for steps 1 through n. As shown below:

[0146] ;

[0147] in, , and All are design parameters; This indicates a design parameter that is greater than zero.

[0148] Furthermore, verifying the stability of the adaptive fixed-time consensus controller includes the following steps:

[0149] Step S41: Select the Lyapunov function from step 1 to step n as:

[0150] ;

[0151] , ;

[0152] ;

[0153] in, , , , All of these represent design parameters that are greater than zero; The Lyapunov function for step 1; Indicates the first Lyapunov function of the step, Denotes the Lyapunov function at step n;

[0154] Step S42: Differentiate the selected Lyapunov function, process it using Young's inequality scaling technique, substitute the virtual control signal and adaptive law, and finally transform the Lyapunov function. The derivative, when rearranged, yields:

[0155] ;

[0156] ;

[0157] ;

[0158] ;

[0159] in, , Represents the set of minimum constant parameters. Represents the Lyapunov function V Power of 1 Represents the set of minimum constant parameters. Represents the Lyapunov function V Power of 1 Represents the known functions of integration. Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, express The upper realm, Indicates the first Virtual control signals for steps, This represents the known function integrated in step n;

[0160] Step S43: Combining mathematical expectation and fixed-time stability theory, we can obtain The expected value and convergence time of the square are as follows:

[0161] ;

[0162] ;

[0163] , , ;

[0164] in, This represents the consistency error (when r=1) or the virtual error signal. Indicates the error convergence time. This represents the maximum error convergence time. Indicates design parameters, Representing Lyapunov functions The expected value.

[0165] To demonstrate the effectiveness of this embodiment, the following simulation verification was performed:

[0166] In the simulation experiment, the network communication topology diagram is as follows: Figure 2 As shown, the follower system model is constructed as follows:

[0167]

[0168] Among them, control input signal The design delay function is as follows: Design the nonlinear function as and .

[0169] The leader system is constructed as follows:

[0170]

[0171] The leader control input is provided by a person (to change the trajectory of the leader's output signal), and is designed as follows: .

[0172] The initial state values ​​of the system are selected as follows: , , , , , , ,and Other design parameters are selected as follows: , , , , , , , , , , , , , , , , , , , , , , , , , .

[0173] Based on the mathematical model constructed above, the control method proposed in this embodiment was applied to the Matlab simulation software for simulation, and the simulation results were obtained, such as... Figure 4-7 As shown. Among them, Figure 4 Output signals for the four follower systems and leader system output signals A diagram illustrating the effectiveness of consistency tracking control; Figure 5 Consistency error It can be seen that the adaptive fixed-time consistency control method based on the auxiliary compensation system can achieve high-precision control effect; Figure 6 For filtering error Simulation results; Figure 7 For follower system control input The simulation results.

[0174] This embodiment uses a backstepping recursive method as the control design framework and proposes an adaptive fixed-time consistency controller based on an auxiliary compensation system to solve the consistency control problem of nonlinear multi-agent systems under time-varying input delays. Simultaneously, by providing and changing the control input signal, the motion trajectory of the multi-agent system can be modified according to requirements. The system model considers time-varying input delays and unknown nonlinear functions, making the system more general. Specifically, an auxiliary compensation system is constructed to handle the unknown time-varying delay function, and a radial basis function neural network is used to approximate the unknown nonlinear function. Furthermore, based on the fixed-time control lemma, a practical fixed-time adaptive consistency control method is proposed to ensure that the consistency error of the multi-agent system converges to a neighborhood near the origin within a fixed time. Based on Lyapunov stability theory, the fixed-time stability of the closed-loop system under the proposed control method is verified.

[0175] A second aspect of the present invention also discloses a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the aforementioned nonlinear multi-agent system fixed-time consistency control method. In an exemplary embodiment, the computer device may further include a transmission device and an input / output device, wherein the transmission device is connected to the processor, and the input / output device is connected to the processor.

[0176] A third aspect of the present invention also discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned nonlinear multi-agent system fixed-time consistency control method. In an exemplary embodiment, the aforementioned computer-readable storage medium may include, but is not limited to, various media capable of storing computer programs, such as a USB flash drive, read-only memory (ROM), random access memory (RAM), portable hard disk, magnetic disk, or optical disk.

[0177] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. All equivalent structural transformations made under the concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A fixed-time consistency control method for nonlinear multi-agent systems, applied to nonlinear multi-agent systems with time-varying input delays, wherein the nonlinear multi-agent system comprises one dynamic leader system with control signals provided by a human and N follower systems, characterized in that: Includes the following steps: S1: Establish a dynamic model and a network communication topology model for the multi-agent system. The dynamic model incorporates an unknown time-varying delay function and a nonlinear function. The dynamic model includes a follower system model, which is as follows: ； in, , ; Represents the system state vector; Indicates the first The first agent of the intelligent agent The derivative of the first-order state; Indicates the first The first agent of the intelligent agent The derivative of the first-order state; Indicates the first The first agent of the intelligent agent Unknown order smooth nonlinear function; Indicates the first The first agent of the intelligent agent The derivative of the first-order state; Indicates a term with delay. The system input signal; Indicates the first The first agent of the intelligent agent Unknown order smooth nonlinear function; Indicates the first The system output signal of each intelligent agent; Indicates the first The first-order system state signal of each agent; S2: Construct an auxiliary compensation system of the same order as the multi-agent system to handle unknown time-varying delay functions, and construct a radial basis function neural network to approximate and handle unknown nonlinear functions; the auxiliary compensation system is: ； in, , Indicates the first The derivative of the first-order auxiliary compensation signal of each agent; ; Indicates the first The second-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Represents a symbolic function; Indicates the first The first-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Indicates the first The derivative of the second-order auxiliary compensation signal of the agent; Indicates the first The third-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; Indicates the first The first intelligent agent The derivative of the first-order auxiliary compensation signal; Indicates the first The first agent of the intelligent agent Step-by-step auxiliary compensation signal; Indicates a design parameter that is greater than zero; Indicates the first The first agent of the intelligent agent Step-by-step auxiliary compensation signal; Indicates a design parameter that is greater than zero; Indicates the first The first agent of the intelligent agent Auxiliary compensation signal; Indicates the first The derivative of the nth-order auxiliary compensation signal of an agent; This represents the difference between the control input and the control output. ; Indicates the control input signal; Indicates a design parameter that is greater than zero; Indicates the first The nth-order auxiliary compensation signal for each agent; Indicates a design parameter that is greater than zero; Indicates the first The first agent of the intelligent agent Auxiliary compensation signal; Indicates a design parameter that is greater than zero; S3: Based on the actual fixed-time stability theory, an adaptive fixed-time consistency controller based on an auxiliary compensation system is constructed using the backstepping method; a nonlinear filter is introduced to estimate the virtual control signal. S4: Verify the stability of the adaptive fixed-time consistency controller based on Lyapunov and fixed-time stability theory.

2. The fixed-time consistency control method for nonlinear multi-agent systems according to claim 1, characterized in that: The dynamics model includes a leader system model; The leader system model is as follows: ； in, The derivative of the leader system state signal; This represents a continuous and bounded control input signal; Indicates the leader system status signal; Indicates the input parameters of the leader system; This indicates the output signal of the leader system.

3. The fixed-time consistency control method for nonlinear multi-agent systems according to claim 1, characterized in that: The leader system is marked as 0, and the follower system is marked as... ; Network communication topology model express, For inclusion A directed graph with n nodes, where Represents a set of nodes. Represents the set of edges; Representing the self To the self Transmitting information; nodes Represents a node Adjacent nodes; make Represent the adjacency matrix, when hour, ;when hour, ; node The set of adjacent nodes is ; definition For the first The in-degree matrix of each autonomous entity, where ; Define the Laplace matrix as The root node is defined as the leader node. ; When the subject When obtaining leader information, define Assume that at least one self-entity possesses a directed path to every other node, i.e., a directed graph. It has a spanning tree.

4. The fixed-time consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: The radial basis function neural network is: definition To be compact A continuous function on the following radial basis function neural network. It can be used to approximate functions : ;in, This represents the ideal weight vector with o being the number of elements in the neural network; Let be the input vector, and This represents the input dimension of the neural network; Indicates network reconstruction error. Represents a constant greater than zero; Represents a basis function vector; Define the optimal weight vector as: ； Design a Gaussian function for: ， ； in, Indicates the center of the receiving field. This represents the width of the Gaussian function.

5. The fixed-time consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: Constructing an adaptive fixed-time consistency controller based on an auxiliary compensation system includes the following steps: Step S31: Define the consistency error of a multi-agent system as: ； in, and ; Indicates the first The output signal of each intelligent agent; This indicates the output signal of the leader system; Indicates the first The output signal of each intelligent agent; Indicates the first The connection coefficient between each agent and the leader; The coordinate transformation design is as follows: ； in, Indicates based on Compensated consistency error Indicates virtual error. ; Indicates the filtered output signal. Indicates virtual control signal, This represents the filtering error signal in a nonlinear filter; Indicates the first The first agent of the intelligent agent System state; After differentiating the consistency error signal, the following nonlinear function is constructed: ； ， ； ； Represents the integrated nonlinear function. Indicates the first The first-order nonlinear function of an agent Indicates the first The second-order system state of an agent, Indicates the first The first-order nonlinear function of an agent express Design parameters, This indicates a design parameter that is greater than zero. Represents the integrated nonlinear function. Indicates the first The first agent of the intelligent agent Order-order nonlinear function, This indicates a design parameter that is greater than zero. Represents the integrated nonlinear function. Indicates the first The nth-order nonlinear function of an agent Indicates a design parameter that is greater than zero; Using radial basis function neural networks to approximate nonlinear functions , and ,Right now: ； in, , Represents the integrated state vector. , ; Step S32: Construct a nonlinear filter and filter parameter update law As shown below: ； in, and Indicates the filter parameters; Indicate the design parameters, satisfying ,and and All are natural numbers; express The estimated value, express The upper realm, Indicates the first The first intelligent agent The absolute value of the derivative of the first-order virtual control signal; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; express The initial value of the estimate; Step S33: Design the virtual control signals for steps 1 to n-1 by selecting the appropriate Lyapunov function. and adaptive fixed-time consistency controller As shown below: ； in, This represents the virtual control signal for step 1; Indicates a design parameter that is greater than zero; express; express The estimated value, , This represents the ideal weighted state value; , representing the integrated state vector; Indicates the first The first-order system state of each agent; ； in, =2,…,n-1; Indicates the first Virtual control signals for each step; Indicates a design parameter that is greater than zero; Indicates a design parameter that is greater than zero; express The estimated value, , This represents the ideal weighted state value; Represents the integrated state vector, and ; ； in, ,and , ; Indicates a design parameter that is greater than zero; Indicates a virtual error signal; This indicates the filtering error signal; Indicates filter design parameters that are greater than zero; Indicates filter design parameters that are greater than zero; Indicates a design parameter that is greater than zero; Represents the integrated state vector. ,and ; express The estimated value, express The upper realm, This represents the derivative of the virtual control signal at step n; express The estimated value, , This represents the ideal weighted state value; Design the adaptive law for steps 1 through n. As shown below: ； in, , and All are design parameters; This indicates a design parameter that is greater than zero.

6. The fixed-time consistency control method for a nonlinear multi-agent system according to claim 1, characterized in that: Verifying the stability of an adaptive fixed-time consensus controller involves the following steps: Step S41: Select the Lyapunov function from step 1 to step n as: ； ， ； ； in, , , , All of these represent design parameters that are greater than zero; The Lyapunov function for step 1; Indicates the first Lyapunov function of the step, Denotes the Lyapunov function at step n; Step S42: Differentiate the selected Lyapunov function, process it using Young's inequality scaling technique, substitute the virtual control signal and adaptive law, and finally transform the Lyapunov function. The derivative, when rearranged, yields: ； ； ； ； in, , Represents the set of minimum constant parameters. Represents the Lyapunov function V Power of 1 Represents the set of minimum constant parameters. Represents the Lyapunov function V Power of 1 Represents the known functions of integration. Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, Indicates design parameters, express The upper realm, Indicates the first Virtual control signals for steps, This represents the known function integrated in step n; Step S43: Combining mathematical expectation and fixed-time stability theory, we can obtain The expected value and convergence time of the square are as follows: ； ； ， ， ； in, This represents the consistency error (when r=1) or the virtual error signal. Indicates the error convergence time. This represents the maximum error convergence time. Indicates design parameters, Representing Lyapunov functions The expected value.

7. A computer device, characterized in that: It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method according to any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method described in any one of claims 1-6.

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