Nonlinear high-order full-state feedback distributed containment control method for multi-agent systems

Abstract

The application belongs to the technical field of multi-agent distributed containment control, and specifically discloses a distributed containment control method for a nonlinear high-order full-drive multi-agent system, which comprises the following steps: a generator is designed, and a dynamic signal of a follower agent is calculated; a nonlinear system function is transformed and evaluated; a controller is designed according to the self properties of the follower agent, and a control signal is calculated; the follower agent moves along a reference trajectory through the control signal; and the method has the following advantages: considering a high-order full-drive multi-agent system under a directed graph condition, an actual system model is directly obtained based on physical laws, the obtained system model is directly controlled, and the system containing completely unknown nonlinear functions is comprehensively considered; the modeling process and the calculation complexity are considered; the distributed containment control problem of the nonlinear high-order full-drive multi-agent under the condition of containing completely unknown nonlinear functions is solved; and the control performance is improved.

Description

Technical Field

[0001] This invention relates to the field of distributed inclusive control technology for multi-agent systems, and more specifically, to a distributed inclusive control method for nonlinear high-order all-drive multi-agent systems. Background Technology

[0002] Over the past few decades, the coordination and control problem of multi-agent systems (MAS) has been extensively studied by many experts and scholars due to the combination of MAS and graph theory and their widespread application in the real world. Examples include formation flying, autonomous underwater vehicle control, and safety issues. In this field, distributed containment control is extremely important. Distributed containment control refers to designing control protocols that ensure the trajectories of followers enter the convex hull formed by the leader's trajectory. Research on distributed containment control methods for linear MAS has yielded fruitful results and has been widely applied in areas such as military reconnaissance, hazardous area detection, target acquisition, battlefield management, fire support, electronic jamming, and communication relay.

[0003] However, the shortcomings of traditional control methods in designing multi-agent distributed inclusive controllers are mainly reflected in the following aspects:

[0004] (1) When designing a control system based on the traditional state-space description method, the high-order system model is usually transformed into an augmented first-order system model, and then the controller is designed for the transformed system. This modeling process will increase the workload to some extent and make the intermediate controller design process more complicated. For example, in the Lyapunov backstepping process, the number of virtual control derivatives will be increased, which will increase the amount of computation.

[0005] (2) Based on the traditional distributed inclusive control strategy, the requirements for communication topology are more stringent. Therefore, many control methods can only meet specific scenarios and cannot be successfully used in actual scenarios.

[0006] (3) The parameter adjustment of the controller designed based on the traditional control method is heavily dependent on the unknown nonlinear function of the system. In actual flight control, due to the existence of completely unknown system functions, the flight control performance is often difficult to achieve the desired control effect. The parameter adjustment of the controller designed based on this strategy is time-consuming and laborious.

[0007] To address these issues, a distributed inclusive control method for nonlinear high-order all-drive multi-agent systems is proposed. Summary of the Invention

[0008] The present invention aims to provide a distributed inclusive control method for nonlinear high-order all-drive multi-agent systems to solve or improve at least one of the above-mentioned technical problems.

[0009] In view of this, a first aspect of the present invention is to provide a distributed inclusive control method for a nonlinear high-order all-drive multi-agent system.

[0010] A second aspect of the present invention is to provide a nonlinear high-order all-drive multi-agent system.

[0011] The first aspect of the present invention provides a distributed inclusive control method for a nonlinear high-order all-drive multi-agent system, comprising the following steps: S1: designing a generator to convert the tracking error of a follower agent moving along a reference trajectory into an output signal. The generator generates a reference signal for the follower agent based on the output signal and the communication information between the follower agent that outputs the output signal and the leader agent and / or the follower agents; S2: converting a nonlinear system function containing the derivative of the system state into a product of a basis vector and a weight vector using a radial basis function neural network. The product and the nonlinear system function have an error. An adaptive neural network is used to obtain an estimate of the weight vector and the error. An adaptive law is designed and the estimate is optimized; S3: using a solver to consider the inherent properties of the follower agent to obtain a positive definite matrix and a parameter matrix, which are used to design a controller for the follower agent. The controller calculates and generates a control signal using the optimized estimate; S4: inputting the control signal into an actuator to make the follower agent move along the reference signal.

[0012] This invention provides a distributed inclusive control method for nonlinear high-order fully driven multi-agent systems. Considering directed graph conditions, it directly obtains the actual system model based on physical laws and directly controls the obtained model. Simultaneously, considering the case where the system contains completely unknown nonlinear functions, it proposes a high-order fully driven distributed inclusive control algorithm based on adaptive neural networks. This overcomes the shortcomings of traditional strategies in terms of modeling process and computational complexity, solves the distributed inclusive control problem of nonlinear high-order fully driven multi-agent systems with completely unknown nonlinear functions, reduces controller design complexity, improves control performance, and enhances system safety and reliability.

[0013] Specifically, the containment control refers to the convergence of follower agents into the convex hull formed by the leader agent. This problem is called encirclement control, containment control, or containment control.

[0014] Specifically, the reference signal is the trajectory of the follower agent as it moves with the leader agent.

[0015] Specifically, the intrinsic property is the omnidirectional nature of the follower agent. An adaptive law is designed and the estimated value is optimized.

[0016] Specifically, an adaptive law is designed and the estimated value is optimized, and the accuracy of the estimated value is optimized to reduce the error.

[0017] In addition, the technical solutions provided by embodiments of the present invention may also have the following additional technical features:

[0018] In any of the above technical solutions, the multi-agent system includes at least two leader agents, and the space encompassed by the output trajectory of the leader agent constitutes a convex hull.

[0019] When the follower agents move along the reference trajectory following the leader agent, all the follower agents are located within the space formed by the convex hull along the vertical direction.

[0020] In this technical solution, the trajectory of the follower agent will enter the convex hull formed by the trajectory of the leader agent. On the one hand, the trajectory of the leader agent can serve as a constraint on the trajectory of the follower agent, such as in the fields of military reconnaissance, danger zone detection, target acquisition, battlefield management, fire support, electronic jamming and communication relay, limiting the activity range of the follower agent. On the other hand, the follower agent will move along the convex hull and thus reach the designated area of ​​the mission.

[0021] In any of the above technical solutions, the communication information is obtained through reference information transmitted between the follower agent and the follower agent capable of exchanging information with it, and the output signal is the error of the reference signal generated between the follower agents; and / or the communication information is obtained through reference information transmitted between the follower agent and the leader agent capable of exchanging information with it, and the output signal is the error of the reference signal generated between the follower agent and the leader agent.

[0022] In this technical solution, the current follower agent only needs to receive the one-dimensional output information of the reference generator of its neighboring follower agents and the output information of the connected leader agent, and generates the reference trajectory of the current follower agent through distributed error, without needing the multi-dimensional state information of its neighboring follower agents, thus reducing the communication burden to a certain extent.

[0023] In any of the above technical solutions, the generator includes a generation model, specifically the following formula: in, The reference signal generated by the generator, r is the designed positive constant. The input signal for the generator includes: an output signal and communication information; and Calculate using the following formula: in, The reference signal for other follower agents is y, where N is the number of follower agents, M is the number of leader agents, and y is the number of leader agents. j For the output signals of the leader intelligent agent, i = 1, 2, ..., N represents the follower agent ID, j = 1, 2, ..., N+M represents the IDs of all agents. for The derivative of .

[0024] In this technical solution, the generator generates the reference trajectory of the current follower agent by using the output information of the neighbor agents. The role of the parameter in the generator is to use only the output information of the agents communicating with the current follower agent, rather than the global communication information, thereby reducing the communication burden. The role of the parameter r is to adjust its size so that the tracking error reaches the ideal range.

[0025] In any of the above technical solutions, the nonlinear system function is set as The product in step S2 is given by the following formula: in, Let the weight vector be an unknown vector, and satisfy the following conditions: Θ i The square of the norm of the weight vector, Given the basis vectors, Let be the error between the product and the nonlinear system function, and satisfy . For unknown positive constants, x i All of these represent the system states of the follower agents.

[0026] In this technical solution, the nonlinear system function of each follower agent is different and unknown, and cannot be directly eliminated in the controller design. Therefore, in order to design a controller to offset the negative impact of the unknown nonlinear system function, the technique in S2 is used to transform it into the product form.

[0027] In any of the above technical solutions, the estimated value of the weight vector is obtained by estimating the squared norm, the estimated value of the error is obtained by estimating the positive constant it satisfies, and the adaptive law is the following formula: in, For the square of the norm Θ i The estimate for derivative, Represents positive constants The estimate for derivative of P iL The components of the Lyapunov positive definite matrix satisfy Pi is a symmetric positive definite matrix, I is a unit vector, and n i Let a be the dimension of the state. i b i k i and All are designed positive constants, and k is adjusted. i and To reduce the estimation error of the norm square and positive constant, The vector formed by the tracking error and its derivative.

[0028] In this technical solution, an adaptive method is used to estimate two unknown constants generated after the transformation of the unknown nonlinear system function. The estimated values ​​of the unknown constants are variables, and the adaptive law is expressed as the derivative of the estimated values. The adaptive law is constructed by tracking error, parameter matrix and known basis function vector, and then the output of the adaptive law is used to replace the two unknown constants.

[0029] In any of the above technical solutions, the controller includes a control model, specifically the following formula: Among them, u i For control signals, g i Given the control matrix function, A i (0～1) For the design parameter matrix, for The second derivative, For H i The transpose of .

[0030] In this technical solution, the controller design includes the above-mentioned parameters, the function of which is to adjust their magnitude so that the tracking error reaches the ideal range, the function of the parameter matrix is ​​to stabilize the controller, and the function of the remaining terms is to offset the additional variables in the system.

[0031] In any of the above technical solutions, step S3 specifically includes: S301, calculating and obtaining the positive definite matrix P through the inherent attributes of the follower agent. iL and the corresponding parameter matrix A i (0～n) Specifically, it includes: the A i (0～n) It is obtained by calculation using the following formula: in, and All are arbitrary given constant matrices. The parameter matrix for the design; the P iL It is obtained by calculation using the following formula: Where, μ iIt is a positive constant, and T is the transpose sign; S302, through the positive definite matrix P iL and parameter matrix A i (0～n) Design a controller that corresponds to the attributes of the follower agent; S303, the controller... e i (0～1) and Calculate the control signal u i .

[0032] In this technical solution, the follower intelligent agent system under consideration is a high-order all-drive system, which has all-drive capability. Therefore, the corresponding controller can be directly designed using the high-order all-drive system method. The parameter matrix can be obtained by inference calculation using the high-order all-drive system method, which reduces the computational complexity.

[0033] In any of the above technical solutions, for the Lyapunov function composed of tracking error and estimation error... Its derivative is obtained by the following formula. Optimize: in, By increasing c i and reduce γ i So that the Lyapunov function V i reduce.

[0034] In this technical solution, according to the definition of tracking error variables We can obtain:

[0035] in,

[0036] Selecting the Lyapunov function V i for: Θ i and The adaptive error satisfies and V i The derivative is:

[0037]

[0038] Using Yang's inequality technique, we obtain:

[0039]

[0040]

[0041]

[0042] thereby, ≤-c i V i +γ i

[0043] in, min{} represents the minimum value within the curly braces {}. By increasing c i Decrease γ i This allows for arbitrarily small tracking errors.

[0044] This ensures that the derivative of the selected Lyapunov function can achieve the specified form, thereby proving that the follower agent can enter the convex hull.

[0045] A second aspect of the present invention provides a nonlinear high-order fully driven multi-agent system, including a follower agent and a leader agent. The follower agent includes: a generator, which uses the output information of its neighboring follower agents as input to obtain a reference signal for the current follower agent; a radial basis function neural network, which transforms the nonlinear system function into a product of basis vectors and weight vectors; an adaptive neural network, which uses the product as input to obtain an estimate of the weight vector and the error; a solver, which solves for the positive definite matrix and parameter matrix controller of the current follower agent using a high-order fully driven method, using the parameter matrix, system state, and estimated values ​​as input and a control quantity as output; and an actuator, which uses the output of the controller as input to obtain the control input for system execution.

[0046] In any of the above technical solutions, the nonlinear high-order all-drive multi-agent system further includes: a communication network, which uses the communication topology of all following agents as input to obtain the output of the neighboring following agents of the current following agent; a control system, which uses the output of the actuator as input to obtain the system output; and a sensor, which uses the system output as input to the sensor and outputs the system output to the user.

[0047] The beneficial effects of this invention compared to the prior art are as follows:

[0048] Within the proposed high-order all-drive multi-agent system inclusive control framework, the adaptive neural network control algorithm proposed in this invention is used to generate a reference signal by designing the generator of the current follower agent. This ensures that the trajectory of the current follower agent converges to the generated reference signal, thus achieving inclusive control of the given leader trajectory. This effectively achieves inclusive control of the given leader trajectory.

[0049] Based on the algorithm of this invention, controller design is directly developed for physical models that are widely existing in reality, making it easier to implement in engineering.

[0050] This algorithm ensures comprehensive control of high-order all-drive multi-agent systems while estimating unknown nonlinear system functions through adaptive neural network technology. Therefore, its precise expression is not required, and thus there is no need to obtain the precise expression of the nonlinear system function.

[0051] The high-order all-drive multi-agent system control method proposed in this invention can be directly applied to practical systems that satisfy various dynamic equations. The system considered is a high-order all-drive system, which is a high-order system structure generated by satisfying dynamic equations. The method proposed in this invention does not require transforming the high-order system into a first-order system for study, but directly performs controller design, thus reducing the computation time of the system transformation process. It eliminates the need for system model transformation, greatly reducing the computational burden and improving efficiency.

[0052] Additional aspects and advantages of embodiments of the invention will become apparent in the following description or may be learned by practice of embodiments of the invention. Attached Figure Description

[0053] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0054] Figure 1 This is a flowchart of the steps of the present invention;

[0055] Figure 2 This is a communication topology diagram of the follower and leader in the simulation experiment of this invention;

[0056] Figure 3 This is a schematic diagram of the process of the present invention;

[0057] Figure 4 In the relationship of the convex hull of the present invention Figure 3 A ranking diagram of the various intelligent agents;

[0058] Figure 5 This is a schematic diagram of the adaptive law curve of the present invention;

[0059] Figure 6 This is a schematic diagram of the system output and state curves of the present invention;

[0060] Figure 7 This is a schematic diagram of the system control input curve of the present invention. Detailed Implementation

[0061] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0062] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0063] Please see Figure 1-7 The following describes a distributed inclusive control method for a nonlinear high-order all-drive multi-agent system according to some embodiments of the present invention.

[0064] An embodiment of the first aspect of this invention proposes a distributed inclusive control method for nonlinear high-order all-drive multi-agent systems. In some embodiments of this invention, such as... Figure 1-6 As shown, a distributed inclusive control method for a nonlinear high-order all-drive multi-agent system is provided. This method includes the following steps:

[0065] Part 1, Reference Trajectory Generator Design: The dynamic signal of the reference trajectory generator is constructed using the communication information between follower agents. The tracking error of each follower agent is designed to track the input signal of the reference trajectory generator. Through ingenious construction and Lyapunov stability analysis, it can be proven that the follower agents can enter the convex hull formed by the outputs of multiple leader agents.

[0066] The second part, the estimation process, involves an adaptive neural network approximating the completely unknown system function. A radial basis function neural network transforms the completely unknown nonlinear system function into a form where known basis vectors are multiplied by unknown weight vectors. The components of the basis vectors can be chosen as Gaussian functions. To obtain the optimal weight vector, an adaptive method is used to adjust the approximation error and the estimated value of the weight vector.

[0067] Part 3, Controller Design: The high-order full-drive system method is used to design corresponding controllers for each follower agent. It is not necessary to convert the high-order system into a first-order system model with state space description. Relatively speaking, the configuration parameters can be arbitrarily selected. Based on the configuration parameters, the positive definite matrix and corresponding parameter matrix that make the system stable can be easily solved by inferring the high-order full-drive method.

[0068] Finally, to verify the effectiveness of the algorithm proposed in this invention, a system was built as follows: Figure 2 The MATLAB / Simulink simulation system shown consists of five follower agents and three leader agents, representing inclusive control.

[0069] This invention takes high-order all-drive system control theory as the main research method and proposes a high-order all-drive distributed inclusive control algorithm based on adaptive neural network. The specific implementation process is as follows.

[0070] The first step, the design method of the reference trajectory generator, is as follows:

[0071] First, define the reference generator dynamics as follows:

[0072]

[0073] Where r is a positive constant of the design. It is the reference signal (the output signal of the reference generator). It is the input signal of the reference generator.

[0074] This represents the reference signal of other follower agents, where N is the number of follower agents, M is the number of leader agents, and y... j This is the output of the leader agent; then, the corresponding Lyapunov function V is defined. ξ for (E is a positive definite diagonal matrix) V represents the vector formed by all the input signals of the reference generator. ξ The derivative is:

[0075]

[0076] Where L1 and L2 are Laplace matrix components, L1 represents the connectivity between the various follower agents, and L2 represents the connectivity between the follower agents and the leader agent. L It is the output of the leader agent, κ and Are positive constants that satisfy y L =[y N+1 ,y N+2 ,…,y N+M ] T This represents the vector formed by the output signals of all leader agents. Based on the above formula, we can obtain: λ max (E) represents the largest eigenvalue of matrix E, λ min (E) represents the smallest eigenvalue of matrix E, and this inequality plays an important role in the final stability analysis.

[0077] The second step, the estimation process, is as follows:

[0078] The system expression is:

[0079]

[0080] in, For the system state, n i Let be the system order of the i-th follower agent. This represents a vector composed of the various orders of the system states. and These are system input and system output, respectively, m i This is represented by the dimension of the system output. It is an unknown nonlinear system function that satisfies f(0). i =0. It is known that the control matrix function satisfies that its determinant is not zero. (C) i The output matrix, or observation matrix, represents how the output variables react to the state variables. Without loss of generality, this invention considers the case where n=2. Since the system contains a completely unknown nonlinear system function, its influence cannot be directly eliminated in the controller design. Therefore, adaptive neural network technology is used for processing. First, the unknown system function is approximated using a radial basis function neural network approximation technique as follows:

[0081]

[0082] in, Represented as an unknown weight vector, Represented as known basis vectors (which can be represented using Gaussian functions), The estimation error of the unknown nonlinear system function is expressed as satisfying in Since is an unknown positive constant, to eliminate the influence of the unknown weight vector and approximation error, an adaptive law is further designed using an adaptive method:

[0083]

[0084] in, This indicates the unknown parameter Θ i Estimate It is the squared norm of the unknown weight vector. Indicates the unknown parameter The estimate, P iL The components of the Lyapunov positive definite matrix satisfy... (Pi is a symmetric positive definite matrix) I represents a unit vector, a i b i k i and It is a positive constant in the design. i b i In controller design, by adjusting k i , This makes the estimation error of the weight vector and the estimation error of the unknown nonlinear system function arbitrarily small.

[0085] Then, the system was rewritten as:

[0086]

[0087] in, This represents a vector consisting of the system state and its first derivative;

[0088] The third step, the specific method for controller design, is as follows:

[0089] First, the controller designed using the high-order all-drive method is as follows:

[0090]

[0091] in, Let A be the parameter matrix of the controller to be designed. i1 A i2 The matrix formed, where This indicates that the tracking error e i (0～1) The tracking error variable is defined as a vector consisting of its first derivative and the vector of its first derivative: To obtain the solution for the design parameters in the controller, the following high-order all-drive system method is used for deduction:

[0092] Given any as well as All are arbitrary given constant matrices. For the designed parameter matrix, the following equation holds:

[0093]

[0094] in, It is the parameter matrix of the design, and then according to the matrix inequality Solve for Pi, where μ i It is a positive number, according to Solving for P iL According to the definition of tracking error variables We can obtain:

[0095] in,

[0096] Selecting the Lyapunov function V i for: Θ i and The adaptive error satisfies and V i The derivative is:

[0097]

[0098] Using Yang's inequality technique, we obtain:

[0099]

[0100]

[0101]

[0102] thereby, ≤-c i V i +γ i

[0103] in, min{} represents the minimum value within the curly braces {}. By increasing c i Decrease γ i This allows for arbitrarily small tracking errors.

[0104] Example 1

[0105] Building such Figure 3 and 4 The MATLAB / Simulink simulation system of inclusive control consisting of five follower agents and three leader agents is shown to verify the effectiveness of the algorithm proposed in this invention:

[0106] First, as follows Figure 3 The leader-follower containment control system with the shown topology was integrated and designed in Matlab / Simulink, and simulation experiments were conducted. The main simulation process is as follows:

[0107] (1) Parameter settings

[0108] First, the output trajector of the leader agent is chosen as: y6 = 1 + 0.5sin(0.5πt), y7 = -1 + 0.5sin(0.5πt), y8 = -0.1 + 0.5sin(0.5πt); second, the basis functions of the neural network are chosen as follows: The initial values ​​and other design parameters are x1(0) = 0.1, x2(0) = 0.15, x3(0) = 0.2, x4(0) = 0.25, x5(0) = 0.3. i = 1, 2, 3, 4, 5, r = 1, a i =1,b i =1,k i =1, The controller design parameter is selected as μ. i =4, η i =

[11] Solving for the solution, we get

[0109] (2) Results Analysis

[0110] Analysis results show that, within the proposed nonlinear high-order all-driven multi-agent inclusive control framework, the high-order all-driven distributed inclusive control algorithm using the adaptive neural network proposed in this invention can effectively achieve inclusive control of a given leader agent reference trajectory. Figure 5 The output change curves of the follower agent and the leader agent are given. It can be clearly seen from the figure that the output trajectory of the follower agent enters the convex hull formed by the output of the leader agent. Figure 6 The curves showing the variation of the estimated values ​​of the ideal weight vector of the neural network and the approximation error are presented. It can be seen from these curves that the adaptive algorithm proposed in this invention can estimate the unknown parameter vector very well. Figure 7 The curves showing the changes in the control input of each follower agent are presented. It can be seen from these curves that the consistency-inclusive controller proposed in this invention requires less energy and has a rapid convergence speed.

[0111] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this invention, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0112] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A distributed inclusive control method using a nonlinear high-order all-drive multi-agent system, characterized in that, Includes the following steps: S1: Design a generator to convert the tracking error of the follower agent moving along the reference trajectory into an output signal. The generator generates the reference signal of the follower agent based on the output signal and the communication information between the follower agent that outputs the output signal and the leader agent and / or the follower agent. S2: The nonlinear system function containing the derivative of the system state is transformed into the product of the basis vector and the weight vector by the radial basis function neural network. There is an error between the product and the nonlinear system function. An adaptive neural network is used to obtain the estimated values ​​of the weight vector and the error. An adaptive law is designed and the estimated values ​​are optimized. S3: Using a solver to consider the inherent properties of the follower agent, the positive definite matrix and parameter matrix of the current follower agent are obtained through a high-order full-drive method, and used to design the controller of the follower agent. The controller calculates and generates control signals based on the optimized estimated values. S4: Input the control signal into the actuator to make the follower agent move along the reference signal; The multi-agent system includes at least two leader agents, and the space encompassed by the output trajectories of the leader agents forms a convex hull. When the follower agents move along the reference trajectory following the leader agent, all the follower agents are located within the space formed by the convex hull along the vertical direction.

2. The distributed containment control method according to claim 1, characterized in that, The generator includes a generative model, specifically the following formula: ； in, The reference signal generated by the generator, r is the designed positive constant. The input signal for the generator includes: an output signal and communication information; and Calculate using the following formula: ； in, The reference signal for other follower agents is N, where N is the number of follower agents and M is the number of leader agents. For the output signals of the leader intelligent agent, i = 1, 2, ..., N represents the follower agent ID, j = 1, 2, ..., N+M represents the IDs of all agents. for The derivative of .

3. The distributed containment control method according to claim 2, characterized in that, The nonlinear system function is defined as follows: The product in step S2 is given by the following formula: ； in, Let the weight vector be an unknown vector, and satisfy the following conditions: , The square of the norm of the weight vector, Given the basis vectors, Let be the error between the product and the nonlinear system function, and satisfy . , For unknown positive constants, All of these represent the system states of the follower agents.

4. The distributed containment control method according to claim 3, characterized in that, The estimated value of the weight vector is obtained by estimating the squared norm, and the estimated value of the error is obtained by estimating the positive constant it satisfies; and The adaptive law is given by the following formula: ； in, For the square of the norm The estimate for The derivative, Represents positive constants The estimate for The derivative, The components of the Lyapunov positive definite matrix satisfy Pi is a symmetric positive definite matrix. For unit vectors, The dimension of the state, , , and All are design constants, and adjusted accordingly. and To reduce the estimation error of the norm square and positive constant, The vector formed by the tracking error and its derivative. .

5. The distributed containment control method according to claim 4, characterized in that, The controller includes a control model, specifically the following formula: ； in, For control signals, Given the control matrix function, For the design parameter matrix, for The second derivative, for The transpose of .

6. The distributed containment control method according to claim 5, characterized in that, The steps in S3 specifically include: S301, calculate and obtain the positive definite matrix through the attributes of the follower agent. and the corresponding parameter matrix Specifically, it includes: The It is obtained by calculation using the following formula: ； in, and All are arbitrary given constant matrices. The parameter matrix for the design; The It is obtained by calculation using the following formula: ； in, It is a positive constant, and T is the transpose sign; S302, through the positive definite matrix and parameter matrix Design a controller that corresponds to the properties of the follower agent; S303, the controller via , , and Calculate the control signal .

7. The distributed containment control method according to claim 6, characterized in that, The Lyapunov function is constructed by combining the tracking error and the estimation error. Furthermore, by optimizing the Lyapunov function to reduce tracking and estimation errors, its derivative is obtained using the following formula. Optimize: ； in, , ; By increasing and adjust smaller So that the Lyapunov function reduce.

8. A nonlinear high-order all-drive multi-agent system implementing the distributed inclusive control method according to any one of claims 1-7, characterized in that, It includes follower agents and leader agents, wherein the follower agents include: The generator takes the output information of the neighboring follower agents as input to obtain the reference signal of the current follower agent; Radial basis function neural networks are used to transform nonlinear system functions into the product of basis vectors and weight vectors; An adaptive neural network takes a product as input and obtains an estimate of the weight vector and the error. The solver solves for the positive definite matrix and parameter matrix of the current follower agent using a high-order full-drive method; The controller takes the parameter matrix, system state, and estimated values ​​as inputs and the control quantity as output. An actuator obtains the control input for system execution by taking the output of the controller as its input.

9. The nonlinear high-order all-drive multi-agent system according to claim 8, characterized in that, Also includes: The communication network takes the communication topology of all follower agents as input and obtains the output of the neighboring follower agents of the current follower agent. A control system uses the output of the actuator as the input to the control system and obtains the system output. The sensor takes the system output as its input and outputs the system output to the user.

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