Distributed preset time fault-tolerant time-varying formation tracking method and system for high-order multi-agent system

Abstract

The invention discloses a distributed preset time fault-tolerant time-varying formation tracking method and system for a high-order multi-agent system, and relates to the technical field of robots, and the method comprises the steps: building a dynamic model of the multi-agent system according to the external disturbance of a follower agent and the influence of an actuator fault; based on the dynamic model of the multi-agent system, time-varying formation description of the multi-agents is established; according to the dynamic model of the multi-agent system and the time-varying formation description, a preset time fault-tolerant time-varying formation tracking controller is constructed based on formation control strategy design analysis; and according to the time-varying formation tracking task, based on a preset time fault-tolerant time-varying formation tracking controller, controlling a follower agent. The fault-tolerant performance and the expansibility of the multi-agent system are improved.

Description

Technical Field

[0001] The present application relates to the field of robotics, and in particular to a distributed preset time fault-tolerant time-varying formation tracking method and system for a high-order multi-agent system. Background Art

[0002] In recent years, multi-agent systems, owing to their collaborative flexibility and robustness, have played an irreplaceable role in fields such as emergency rescue and intelligent transportation. Typical applications, such as drone swarms, unmanned boat formations, and micro-nano satellite networks, all rely on efficient formation control technologies to achieve key tasks such as coordinated reconnaissance, dynamic interception, and distributed detection. As mission complexity increases, time-varying formation tracking control has become a crucial approach to enhancing the adaptability and mission execution capabilities of multi-agent systems. Research on this topic holds significant strategic value in advancing the practical and intelligent development of intelligent swarm technology.

[0003] However, in practical applications, multi-agent systems often face uncertainties such as actuator failures and external interference, making it difficult for traditional control methods to balance fault tolerance and dynamic performance. Existing research has significant limitations: asymptotically stable control cannot meet the finite time convergence requirements, and fixed-time control is limited in practicality due to conservative time estimates and excessive initial inputs. Especially in high-order linear multi-agent systems, there is still a lack of systematic solutions for how to achieve fault-tolerant formation tracking under precise constraints of preset time. Breaking through this technical bottleneck is crucial to improving the reliability and response speed of the system in complex environments, and is a cutting-edge direction that urgently needs to be explored in depth. Summary of the Invention

[0004] The purpose of this application is to provide a distributed preset time fault-tolerant time-varying formation tracking method and system for a high-order multi-agent system, which can improve the fault tolerance and scalability of the multi-agent system.

[0005] To achieve the above objectives, this application provides the following solutions:

[0006] In a first aspect, the present application provides a distributed preset time fault-tolerant time-varying formation tracking method for a high-order multi-agent system, comprising:

[0007] According to the influence of external disturbances and actuator failures on follower agents, a dynamic model of the multi-agent system is established;

[0008] Based on the dynamic model of multi-agent system, a time-varying formation description of multi-agent is established;

[0009] According to the dynamic model of the multi-agent system and the time-varying formation description, based on the formation control strategy design analysis, a preset time fault-tolerant time-varying formation tracking controller is constructed;

[0010] According to the time-varying formation tracking task, the follower agent is controlled based on the preset time-tolerant time-varying formation tracking controller.

[0011] Optionally, the dynamic model of the multi-agent system includes a leader dynamic model and a follower dynamic model;

[0012] The formula expression of the leader dynamics model is:

[0013]

[0014] in, Indicates the status of the leader;

[0015] The formula expression of the follower dynamics model is:

[0016]

[0017] in, represents the state of follower i, represents the set of integers from a to b, represents n-dimensional space, Represents an m-dimensional space, n represents that the state of each agent is an n-dimensional vector, represents the output of the failed actuator of follower i; represents the unknown external disturbance suffered by follower i; represents the system matrix, represents the control matrix; represents the control input of the actuator of follower i; represents the unknown output deviation of the actuator of follower i; the actuator efficiency factor of follower i is expressed as ρ i (t) = diag{ρ i1 (t),ρ i2 (t),...,ρ im (t)}, 0<ρ ij (t)≤1, represents the unknown efficiency factor of the jth channel of the actuator of follower i, d i (t) represents the impact of external disturbance on the system, and n represents the dimension of the state.

[0018] Optionally, the expression describing the time-varying formation of the multi-agent is:

[0019]

[0020] in, represents the time-varying offset from the state of the i-th follower agent to the state of the leader agent, and T represents the transpose.

[0021] Optionally, the formation control strategy design analysis includes checking formation feasibility conditions, designing time-varying formation compensation terms, designing time-varying parameters and time-varying positive definite gain matrices, calculating time-varying formation tracking local errors, and designing adaptive parameters.

[0022] Optionally, the formula for checking the formation feasibility condition is:

[0023]

[0024] in, and Given the control matrix Sure, and

[0025] Optionally, in designing the time-varying formation compensation term, the formula expression of the time-varying formation compensation term is:

[0026]

[0027] in, represents the state offset h of the i-th follower agent i The first derivative with respect to time.

[0028] Optionally, designing time-varying parameters and a time-varying positive definite gain matrix specifically includes:

[0029] When tr(A)≠0, according to the system matrix A, determine the parameters

[0030] When tr(A)=0, the parameters are determined according to the system matrix A. as well as

[0031] in, λ i (A) represents the i-th eigenvalue of matrix A, Re(λ i (A)) represents its real part; T p represents the pre-set convergence time, α1-α6 represent the control parameters, Represented by the time-varying parameter matrix Q t (t)Correlation coefficient;

[0032] According to the formula And the formula Calculate the positive definite matrix W t , where I n represents the n-dimensional identity matrix;

[0033] According to the formula Design time-varying parameter γ t ;

[0034] According to formula A T Q t +Q t AQ t BB T Q t =-γ t Q t ., determine the time-varying positive definite gain matrix Q t .

[0035] Optionally, the calculation formula for the time-varying formation tracking local error is:

[0036]

[0037] Among them, a ij represents the element in the i-th row and j-th column of the communication topology adjacency matrix of the multi-agent system, N represents the number of follower agents, x j (t) represents the state of the j-th agent.

[0038] Optionally, the solution formula for the adaptive parameter is:

[0039]

[0040] Among them, η 1i , η 2i and η 3i represents any positive constant, and represents the adaptive parameter, e i represents the time-varying formation tracking local error, v i represents the time-varying formation compensation function.

[0041] In a second aspect, the present application provides a high-order multi-agent system distributed preset time fault-tolerant time-varying formation tracking system, comprising:

[0042] The dynamic model building module is used to build a dynamic model of the multi-agent system based on the influence of external disturbances and actuator failures on the follower agents;

[0043] A time-varying formation description building module is used to build a time-varying formation description of multiple agents based on the dynamic model of the multi-agent system;

[0044] A controller construction module is used to construct a preset time-tolerant time-varying formation tracking controller based on the dynamic model of the multi-agent system and the time-varying formation description and on the formation control strategy design analysis;

[0045] The intelligent agent control module is used to control the follower intelligent agent according to the time-varying formation tracking task and based on the preset time-tolerant time-varying formation tracking controller.

[0046] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0047] The present application provides a distributed preset time fault-tolerant time-varying formation tracking method and system for a high-order multi-agent system. First, by considering the external disturbances and actuator failures to which the follower agent is subjected, an accurate multi-agent system dynamics model is established. Based on this model, a time-varying formation description of the multi-agent is further constructed, which enables the system to understand and adapt to changes in the formation. In the controller design stage, the application does not rely on global topology information or upper bound information on faults and interferences, but instead constructs a preset time fault-tolerant time-varying formation tracking controller based on the analysis of the formation control strategy. This controller can automatically adjust the control strategy to cope with unknown external interference and actuator failures. Finally, through the preset time fault-tolerant control strategy, the application can achieve the formation tracking goal within a limited time, and can ensure the stability and performance of the system even in the presence of actuator failures and unknown external interferences. The fault tolerance and reliability of the system are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0049] Figure 1 Schematic diagram of a distributed preset time fault-tolerant time-varying formation tracking method for a high-order multi-agent system in one embodiment of the present application;

[0050] Figure 2 A flow chart of a distributed fault-tolerant preset time-varying formation tracking method for a high-order linear multi-agent system provided in one embodiment of the present application;

[0051] Figure 3 A communication topology diagram of a multi-agent system provided in one embodiment of the present application;

[0052] Figure 4 A state diagram of a multi-agent system at different times provided by an embodiment of the present application;

[0053] Figure 5 A time-varying formation tracking error curve provided by an embodiment of the present application;

[0054] Figure 6A schematic diagram of the functional modules of a distributed preset time fault-tolerant time-varying formation tracking device for a high-order multi-agent system provided in one embodiment of the present application. DETAILED DESCRIPTION

[0055] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0056] In recent years, fast-converging formation control techniques that account for actuator failures have become a research hotspot, attracting considerable attention from experts and scholars. However, to date, relatively few relevant research results have been achieved. In particular, addressing the problem of pre-set-time convergence for high-order systems has been a near-miss, with few researchers making substantial breakthroughs. Wang et al. employed an extended state observer to address the interference-tolerant formation problem for second-order systems; Hua et al. implemented fault compensation for high-order systems based on adaptive control; Huang and Chang improved convergence performance through finite-time and fixed-time control, respectively. However, the former relies on initial conditions, while the latter suffers from parameter conservatism. Yang and Shi et al. further incorporated pre-set-time control into observer design for formation tracking, significantly improving temporal controllability. However, these results are primarily limited to integrator-type systems. Due to the more complex dynamics of more general high-order linear multi-agent systems, existing methods are difficult to generalize. In particular, implementing pre-set-time fault-tolerant formation tracking control for high-order linear multi-agent systems, considering both actuator failures and external disturbances, remains an unresolved open problem.

[0057] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0058] Example 1

[0059] like Figure 1 As shown, this embodiment provides a distributed preset time fault-tolerant time-varying formation tracking method for a high-order multi-agent system, including:

[0060] Step 101: Establish a dynamic model of the multi-agent system based on the influence of external disturbances and actuator failures on the follower agent;

[0061] Step 102: Based on the dynamic model of the multi-agent system, establish a time-varying formation description of the multi-agent;

[0062] Step 103: constructing a preset time-tolerant time-varying formation tracking controller based on the dynamic model of the multi-agent system and the time-varying formation description and the formation control strategy design analysis;

[0063] Step 104: According to the time-varying formation tracking task, the follower agent is controlled based on the preset time-tolerant time-varying formation tracking controller.

[0064] Specifically, this embodiment considers the influence of external disturbances and actuator failures on the follower agent, establishes a dynamic model of the multi-agent system; then establishes a time-varying formation description of the multi-agent; then, based on the system dynamic model and the time-varying formation description, the design of a preset time-tolerant time-varying formation tracking controller is completed by checking the formation feasibility conditions, designing time-varying formation compensation terms, designing time-varying parameters and time-varying positive gain matrices, calculating the local error of time-varying formation tracking, and designing adaptive parameters; finally, the designed controller is used to control the follower agent to complete the time-varying formation tracking task.

[0065] In some embodiments, Figure 2 As shown, when executing steps 101-104, the specific steps may be as follows:

[0066] 1) Establish a dynamic model of a multi-agent system with 1 leader and N followers.

[0067] Among them, the leader's dynamic model:

[0068]

[0069] in, Indicates the status of the leader, represents the system matrix.

[0070] By considering the influence of external disturbances and actuator failures, the dynamic characteristics of the i-th follower are described, that is, the follower dynamic model:

[0071]

[0072] Among them, for represents the state of follower i, represents the set of integers from a to b, represents an n-dimensional space, where each dimension is a value in the real number field, Represents an m-dimensional space, where each dimension is a value in the real number field, and n represents that the state of each agent is an n-dimensional vector. For example, if the position and velocity information of the agent in the x and y directions are selected as the agent state, then the state x of follower i is i (t) is a 4-dimensional vector; represents the output of the failed actuator of follower i; represents the unknown external disturbance suffered by follower i; represents the system matrix, represents the control matrix; represents the control input of the actuator of follower i; represents the unknown output deviation of the actuator of follower i; the actuator efficiency factor of follower i is expressed as ρ i (t) = diag{ρ i1 (t),ρ i2 (t),...,ρ im (t)}, where 0<ρ ij (t)≤1, represents the unknown efficiency factor of the jth channel of the actuator of follower i. i (t) and f bi For different values ​​of (t), the above model can represent typical failure modes such as actuator failure and deviation. i (t) represents the impact of external disturbance on the system.

[0073] 2) Establish a description of the multi-agent time-varying formation. represents the time-varying offset from the state of the ith follower agent to the state of the leader agent, then the entire time-varying formation is represented by the vector Definition, T is the transpose.

[0074] 3) Determine the expression of the preset time-tolerant time-varying formation tracking controller for each follower in the multi-agent system described in 1).

[0075] The formation control strategy design analysis includes checking formation feasibility conditions, designing time-varying formation compensation terms, designing time-varying parameters and time-varying positive definite gain matrices, calculating time-varying formation tracking local errors, and designing adaptive parameters.

[0076] (1) For follower i, check the following formation feasibility conditions:

[0077]

[0078] in, and Given the control matrix and

[0079] If all followers meet the above feasibility conditions, the algorithm continues to execute; otherwise, it indicates that the specified formation h i It is not applicable to the designed controller and the algorithm terminates.

[0080] (2) The time-varying formation compensation term v of follower i is determined by the following formula: i :

[0081]

[0082] (3) Design time-varying parameter γ t and the time-varying positive definite gain matrix Q t .

[0083] First, according to the given system matrix Calculate the following parameters:

[0084] For the case where tr(A)≠0:

[0085]

[0086] For the case of tr(A)=0:

[0087]

[0088] in, λ i (A) represents the i-th eigenvalue of matrix A, Re(λ i (A)) represents its real part; T p is the pre-set convergence time. is the time-varying parameter matrix Q t (t) Correlation coefficient,

[0089] Use the following method to determine: first take a series of γ in a certain range t The value of is solved by the following formula

[0090]

[0091] Then solve the following time-varying parameter Lyapunov equation (TVPLE) to obtain the positive definite matrix W t :

[0092]

[0093] Let κ t =2tr(A)+nγ t , calculate δ t =κ t λ n (W t Q t ),use and You can confirm

[0094] Then, based on the above parameters and the preset time, the time-varying parameter γ is designed using the following formula: t , which is a function related to time t and needs to be updated at each moment:

[0095]

[0096] Finally, the following time-varying parameter Lyapunov equation (TVPLE) is solved to determine the time-varying positive definite gain matrix

[0097] A T Q t +Q t AQ t BB T Q t =-γ t Q t .

[0098] The time-varying positive definite gain matrix Q obtained in this way is t The system formation tracking error can be converged within the preset time.

[0099] (4) Follower agents interact with neighboring nodes to obtain neighbor status information. Each follower i, Compute the time-varying formation tracking local error relative to neighboring nodes:

[0100]

[0101] Among them, a ij Represents the element in the i-th row and j-th column of the communication topology adjacency matrix of the multi-agent system. When agent i can obtain information from agent j, a ij = 1, when agent i cannot obtain information from agent j ij =0.

[0102] Among them, the communication topology of the multi-agent system is as follows: Figure 3 As shown, number 0 represents the leader, and numbers 1, 2, ..., 6 represent followers.

[0103] (5) Design adaptive parameters and They represent the estimates of follower i to actuator failures, external disturbances and global information. Set the initial values ​​for the adaptive parameters, Using the following adaptive parameters and The update law solves the adaptive parameters at each moment:

[0104]

[0105] Among them, η 1i , η 2i and η 3i is any positive constant.

[0106] (6) Design the controller as follows:

[0107] To follower i, Consider the following preset time-tolerant time-varying formation tracking controller:

[0108]

[0109] in,

[0110] Each term in the time-dependent, fault-tolerant, time-varying formation tracking controller has a specific function. The first term is primarily responsible for driving the follower agent to achieve the desired formation and track the leader; the second term is primarily responsible for compensating for the effects of additional terms caused by the time-varying formation; and the third term plays a key role in adaptively compensating for actuator failures and unknown external disturbances.

[0111] Based on the preset time-tolerant time-varying formation tracking controller designed in 9), the control instructions for each follower agent are determined to control the follower's state to follow the leader's state within the preset time and form the desired state formation. Based on the desired time-varying formation, the preset time, the state of the leader agent, and the state of the follower agents, the preset time-varying formation tracking effect of the multi-agent system can be constructed, which can be described as follows:

[0112] For any bounded initial state, the state of each follower i can be realized under the action of the controller in step 2:

[0113]

[0114] ||x i -x0-h i ||=0,t≥T p

[0115] Where ||a|| represents the norm of vector a.

[0116] In some embodiments, as Figure 4 As shown, actuator failure, deviation fault and external interference are added to followers 3, 4 and 5. The preset convergence time T p = 10 seconds. The design requires 6 followers to form a time-varying hexagonal formation. The state of the multi-agent system at different times is as follows: Figure 4 As shown in (a), (b), (c), and (d).

[0117] where x i (t) = [x i1(t),x i2 (t),x i3 (t)] T Indicates followers The leader state is represented by a square, and the remaining six graphs represent the states of the six followers. The trajectory curves in the figure show that after 10 seconds, the followers form a regular hexagonal formation, and the center of the formation tracks the leader's trajectory.

[0118] Definition i =x i -x0-h i Indicates followers The time-varying formation tracking error curve obtained by this method is as follows: Figure 5 As shown in the figure, it can be seen from the curve that all followers can overcome actuator failures and external disturbances, ensuring that the formation tracking error converges within the preset 10s, reflecting that this method achieves the preset time formation tracking control.

[0119] In addition, this application also provides a specific usage scenario.

[0120] In this scenario, a multi-agent system is applied to the coordinated flight missions of a swarm of drones. The leader drone is responsible for planning the overall flight path, while the follower drones are required to form and maintain a specific time-varying formation within a preset time to perform complex missions such as reconnaissance, monitoring, or transportation.

[0121] During the mission, some follower drones may encounter challenges such as actuator failure, deviation faults, or external interference. However, thanks to the preset-time fault-tolerant time-varying formation tracking controller designed in this method, these drones can quickly adjust their states to overcome failures and interference, ensuring that the formation tracking error converges within the preset time.

[0122] When an actuator failure or external disturbance is detected, the adaptive parameters immediately initiate an update law, estimating the extent of the failure and disturbance in real time and compensating for it through adaptive compensation terms in the controller. Simultaneously, the time-varying formation compensation term is adjusted based on the current time-varying formation requirements to ensure that the follower drones accurately track the leader drone's state and form the desired time-varying formation.

[0123] Example 2

[0124] like Figure 6 As shown, this embodiment provides a high-order multi-agent system distributed preset time fault-tolerant time-varying formation tracking system, including:

[0125] A dynamic model building module 601 is used to build a dynamic model of the multi-agent system based on the influence of external disturbances and actuator failures on the follower agents;

[0126] A time-varying formation description building module 602 is used to build a time-varying formation description of the multi-agent system based on the dynamics model of the multi-agent system;

[0127] A controller construction module 603 is configured to construct a preset time-tolerant time-varying formation tracking controller based on the dynamic model of the multi-agent system and the time-varying formation description and on the formation control strategy design analysis;

[0128] The agent control module 604 is used to control the follower agent according to the time-varying formation tracking task and based on the preset time-tolerant time-varying formation tracking controller.

[0129] In summary, this application has the following technical effects:

[0130] In the practical application of time-varying formation tracking control in multi-agent systems, agents may experience actuator failures and deviation faults in complex environments, as well as external disturbances such as wind disturbances and collisions. The occurrence of actuator failures and external disturbances will severely impact the system's formation tracking performance. Furthermore, in practical scenarios, the upper bounds of actuator failures and external disturbances are often unknown to the agents. Existing control methods, such as asymptotic convergence, finite-time convergence, and fixed-time convergence, have various limitations in terms of convergence speed and the conditions required to estimate convergence time, resulting in insufficient ability to estimate and control convergence time.

[0131] This application proposes a distributed, fault-tolerant, preset-time, time-varying formation tracking method for high-order linear multi-agent systems. By introducing adaptive parameters to achieve fully distributed control, each follower autonomously determines the control input in a fully distributed manner, without requiring information about upper bounds on actuator failures and unknown external interference, or global topology information. This improves the system's fault tolerance and scalability. Furthermore, using the preset-time method, the system's formation tracking error converges within a preset time, unaffected by the system's initial state, and the convergence time can be specified by the user.

[0132] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0133] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A distributed preset time fault tolerant time-varying formation tracking method for a high-order multi-agent system, characterized in that: include: According to the influence of external disturbances and actuator failures on follower agents, a dynamic model of the multi-agent system is established; Based on the dynamic model of multi-agent system, a time-varying formation description of multi-agent is established; According to the dynamic model of the multi-agent system and the time-varying formation description, based on the formation control strategy design analysis, a preset time fault-tolerant time-varying formation tracking controller is constructed; According to the time-varying formation tracking task, the follower agent is controlled based on the preset time-tolerant time-varying formation tracking controller.

2. A distributed preset time fault tolerant time-varying formation tracking method for a high-order multi-agent system according to claim 1, characterized in that: The dynamic model of the multi-agent system includes a leader dynamic model and a follower dynamic model; The formula expression of the leader dynamics model is: in, Indicates the status of the leader; The formula expression of the follower dynamics model is: in, represents the state of follower i, represents the set of integers from a to b, represents n-dimensional space, Represents an m-dimensional space, n represents that the state of each agent is an n-dimensional vector, represents the output of the failed actuator of follower i; represents the unknown external disturbance suffered by follower i; represents the system matrix, represents the control matrix; represents the control input of the actuator of follower i; represents the unknown output deviation of the actuator of follower i; the actuator efficiency factor of follower i is expressed as ρ i (t) = diag{ρ i1 (t),ρ i2 (t),...,ρ im (t)}, 0<ρ ij (t)≤1, represents the unknown efficiency factor of the jth channel of the actuator of follower i, d i (t) represents the impact of external disturbance on the system, and n represents the dimension of the state.

3. The method for tracking a high-order multi-agent system in a distributed preset time fault-tolerant time-varying formation according to claim 2, characterized in that: The expression describing the time-varying formation of the multi-agent is: in, represents the time-varying offset from the state of the i-th follower agent to the state of the leader agent, and T represents the transpose.

4. The method for tracking a high-order multi-agent system in a distributed preset time fault-tolerant time-varying formation according to claim 3, characterized in that: The formation control strategy design analysis includes checking formation feasibility conditions, designing time-varying formation compensation terms, designing time-varying parameters and time-varying positive definite gain matrices, calculating time-varying formation tracking local errors, and designing adaptive parameters.

5. The method for tracking a high-order multi-agent system in a distributed preset time fault-tolerant time-varying formation according to claim 4, characterized in that: The formula for checking the feasibility condition of the formation is: in, and Given the control matrix Sure, and 6. The method for tracking a high-order multi-agent system in a distributed preset time fault-tolerant time-varying formation according to claim 5, characterized in that: The formula expression of the time-varying formation compensation term in the design of the time-varying formation compensation term is: in, represents the state offset h of the i-th follower agent i The first derivative with respect to time.

7. The method for tracking a high-order multi-agent system in a distributed preset time fault-tolerant time-varying formation according to claim 6, characterized in that: Design time-varying parameters and time-varying positive definite gain matrices, including: When tr(A)≠0, according to the system matrix A, determine the parameters When tr(A)=0, the parameters are determined according to the system matrix A. as well as in, λ i (A) represents the i-th eigenvalue of matrix A, Re(λ i (A)) represents its real part; T p represents the pre-set convergence time, α1-α6 represent the control parameters, Represented by the time-varying parameter matrix Q t (t) Correlation coefficient; According to the formula And the formula Calculate the positive definite matrix W t , where I n represents the n-dimensional identity matrix; According to the formula Design time-varying parameter γ t ; According to formula A T Q t +Q t AQ t BB T Q t =-γ t Q t ., determine the time-varying positive definite gain matrix Q t .

8. The method for tracking a high-order multi-agent system in a distributed preset time fault-tolerant time-varying formation according to claim 7, characterized in that: The calculation formula for the time-varying formation tracking local error is: Among them, a ij represents the element in the i-th row and j-th column of the communication topology adjacency matrix of the multi-agent system, N represents the number of follower agents, x j (t) represents the state of the j-th agent.

9. The method for tracking a high-order multi-agent system in a distributed preset time fault-tolerant time-varying formation according to claim 8, characterized in that: The solution formula for the adaptive parameters is: Among them, η 1i , η 2i and η 3i represents any positive constant, and represents the adaptive parameter, e i represents the time-varying formation tracking local error, v i represents the time-varying formation compensation function.

10. A high-order multi-agent system distributed preset time fault-tolerant time-varying formation tracking system, characterized by: include: The dynamic model building module is used to build a dynamic model of the multi-agent system based on the influence of external disturbances and actuator failures on the follower agents; A time-varying formation description building module is used to build a time-varying formation description of multiple agents based on the dynamic model of the multi-agent system; A controller construction module is used to construct a preset time-tolerant time-varying formation tracking controller based on the dynamic model of the multi-agent system and the time-varying formation description and on the formation control strategy design analysis; The intelligent agent control module is used to control the follower intelligent agent according to the time-varying formation tracking task and based on the preset time-tolerant time-varying formation tracking controller.

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