Fixed-time sliding mode control method and system for multiple autonomous agents under actuator failures

Abstract

The application relates to a method and system for fixed-time sliding mode control of multiple autonomous bodies under actuator failure, and models of leader and follower autonomous body systems are respectively constructed; a communication relationship between followers and leaders is determined according to a network communication topological structure among the multiple autonomous bodies in a consensus control process of the multiple autonomous body systems; a fixed-time disturbance observer is determined according to estimated unknown external disturbance, fault severity and estimation error; a consensus state error of the i-th follower autonomous body system is defined according to states of the leaders and the followers and the communication relationship among the autonomous bodies, the consensus state error is in a boundary region of a fixed-time preset performance function constraint, and an error model of the multiple autonomous body system is reconstructed according to the consensus error; and a sliding mode control law and an adaptive law under actuator failure and unknown external disturbance are designed based on a set sliding mode surface, and the influence of the actuator failure and the disturbance is compensated.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of artificial intelligence and control technology, in particular to a fixed-time sliding mode control method and system for multiple autonomous agents under actuator failure. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute the prior art.

[0003] A multi-agent system is a system composed of multiple autonomous agents with certain perception, communication, decision-making and action capabilities. Through local information interaction, each agent updates and adjusts its own state, and cooperates with each other to complete complex global tasks. These systems include but are not limited to unmanned aerial vehicle swarms, robot collaboration, and distributed sensor networks. Multi-agent systems have attracted great attention due to their potential in automation, monitoring and complex task processing. In these applications, it is crucial to implement an effective and reliable consensus control strategy that ensures all agents can work together to achieve common goals.

[0004] However, traditional control methods have some inherent limitations when dealing with multi-agent system cooperative control.

[0005] Firstly, traditional control methods often focus on asymptotic stability, which means that the system state will eventually approach the ideal value, but the convergence time cannot be guaranteed and may be very long.

[0006] Secondly, disturbances in practical applications and uncertainties or failures of actuators can severely affect control performance and even lead to system instability.

[0007] In addition, many systems require real-time or near-real-time performance, which requires control strategies to ensure system state convergence within a predetermined strict time.

[0008] To overcome these problems, fixed-time control strategies can guarantee system stability within a fixed time regardless of the initial conditions of the system. This control strategy is particularly important for application scenarios that require fast response. Although fixed-time control strategies are theoretically attractive, their application to multi-agent systems, especially in the presence of unknown disturbances and actuator failures, requires solving a series of problems such as how to design effective control laws without relying on accurate model information and how to achieve reliable information interaction under limited communication resources. SUMMARY

[0009] To solve the technical problems in the background art, the present application provides a method and system for fixed-time sliding mode control of multiple autonomous agents under actuator failure, which combines fixed-time control theory, sliding mode control and event-triggered mechanism, and designs an effective robust cooperative control solution for the multiple autonomous agent system to achieve fast and reliable tracking performance, which can work effectively even in the face of actuator failure and external disturbance. In addition, the introduction of the event-triggered mechanism further reduces the communication demand and improves the practicality and cost-effectiveness of the system.

[0010] To achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0011] The first aspect of the present application provides a method for fixed-time sliding mode control of multiple autonomous agents under actuator failure, comprising the following steps:

[0012] According to the controller input, the nonlinear function and the states of the leader and the follower, the models of the leader and the follower autonomous agent systems are constructed respectively;

[0013] According to the network communication topology between each autonomous agent in the consistency control process of the multiple autonomous agent system, the communication relationship between the follower and the leader is determined;

[0014] According to the estimated unknown external disturbance, the severity of the failure and the estimation error, a fixed-time disturbance observer is determined;

[0015] According to the states of the leader and the follower and the communication relationship between each autonomous agent, the consistency state error of the i-th follower autonomous agent system is defined, which is within the boundary region of the fixed-time preset performance function constraint; according to the defined consistency error, the error model of the multiple autonomous agent system with fixed-time preset performance is reconstructed;

[0016] Based on the set sliding surface, a sliding mode control law and an adaptive law under actuator failure and unknown external disturbance are designed to compensate for the influence of actuator failure and disturbance.

[0017] Further, it also has a dynamic event-triggered mechanism, which is specifically: setting the dynamic event-triggered mechanism of the i-th follower autonomous agent system, defining E i (t)=τ i (t)-u i (t) is the measurement error of the controller output, and the event-triggered condition is constructed as follows:

[0018]

[0019] Where, Ψ i (t)=ι i |E i | 2For the triggering function, ι i satisfies ι i > 0, the dynamic variable χ i is set to and 0 < v 1i < 1, v 2i > 0.

[0020] Further, the model of the leader and follower autonomous body system is specifically as follows:

[0021] The model of the leader autonomous body system is as follows:

[0022]

[0023] Wherein, p0, q0 are the states of the leader, f0(p0, q0) and u0 represent the nonlinear function and the controller input respectively;

[0024] The model of the follower autonomous body system is as follows:

[0025]

[0026] Wherein, p i , q i are the states of the follower, f i (p i , q i ), d i and u i represent the nonlinear function, unknown external disturbance and controller input respectively; ρ i represents the severity of the fault, and satisfies 0 < ρ i < 1.

[0027] Further, according to the network communication topological structure between each autonomous body in the consensus control process of the multi-autonomous body system, the communication relationship between the follower and the leader is determined; specifically as follows:

[0028] The communication relationship between each autonomous body in the consensus fault-tolerant control process of the multi-autonomous body system is described by using an undirected graph

[0029] Wherein, represents the node set of the undirected graph G, represents the edge set of the undirected graph G, represents the adjacency matrix of the undirected graph G; the Laplacian matrix Wherein and

[0030] If the autonomous body i can receive the information of the autonomous body j, then a ij ≠ 0, otherwise, a​ij = 0; B0= diag{b i0} describes the communication relationship between the follower and the leader, if the ith follower agent can receive the information of the leader, then b i0 = 1; otherwise, b i0 = 0.

[0031] Further, the fixed-time disturbance observer is shown as follows:

[0032]

[0033] where k θ1 is the design parameter, is the estimation of p i , p i is the severity of the fault, is the estimation of d i , d i is the unknown external disturbance, and the estimation error is denoted as

[0034] Further, according to the states of the leader and the followers and the communication relationship between the agents, the consensus state error of the ith follower agent system is defined as shown below:

[0035]

[0036] where p0, q0 are the states of the leader, p i , q i , p j , q j are the states of the followers, and if the follower agent i can receive the information of agent j, then b i = 1, otherwise, b i = 0.

[0037] Further, the consensus state error is in the boundary region of the fixed-time preset performance function constraint, specifically:

[0038] The preset performance is set as:

[0039] where is the fixed-time preset performance function, shown as follows:

[0040]

[0041] where l i , and satisfy l i > 1, a normal number.

[0042] Further, according to the defined consistency error, the multi-agent system error model with fixed time preset performance is reconstructed, specifically: the second order error of the multi-agent system with fixed time preset performance is reconstructed to obtain: Wherein, the conversion function is defined as Wherein

[0043] Further, based on the set sliding surface, the sliding mode control law and the adaptive law under the actuator fault and unknown external disturbance are designed, as shown in the following formula:

[0044] The set sliding surface is as shown in the following formula: Wherein, η 1i >0, η 2i >0, k1>2;

[0045] The sliding mode control law and the adaptive law are as shown in the following formula:

[0046]

[0047]

[0048] Wherein, η 3i >0, η 4i >0, ξ i >0, h i >0, v 3i and mu 2i are design parameters.

[0049] The second aspect of the application provides a multi-agent fixed time sliding mode control system under actuator fault, comprising.

[0050] The model construction module is configured to: construct the model of the leader and follower autonomous systems according to the controller input, the nonlinear function and the state of the leader and follower.

[0051] The communication relationship module is configured to: determine the communication relationship between the follower and the leader according to the network communication topological structure between each autonomous agent in the multi-agent system consistency control process.

[0052] The disturbance observer is configured to: determine the fixed time disturbance observer according to the estimated unknown external disturbance, the fault severity and the estimation error.

[0053] An error model is configured to define a consensus state error of the i-th follower autonomous body system according to states of the leader and the followers and a communication relationship between the autonomous bodies, the consensus state error being in a boundary region of a fixed-time preset performance function constraint, and reconstruct a multi-autonomous body system error model with a fixed-time preset performance according to the defined consensus error;

[0054] A fault-tolerant compensation module is configured to design a sliding mode control law and an adaptive law under actuator faults and unknown external disturbances based on a set sliding surface, and compensate for the influence of the actuator faults and the disturbances.

[0055] Compared with the prior art, the above one or more technical solutions have the following beneficial effects:

[0056] 1. The fixed-time control theory and the sliding mode control are combined to design an effective robust cooperative control solution for the multi-autonomous body system, which can cope with uncertainties and external disturbances, enhance the anti-interference ability and control accuracy of the system, ensure smooth and accurate control, and achieve fast and reliable tracking performance, even when facing actuator faults and external disturbances.

[0057] 2. The introduction of the event-triggered mechanism further reduces the communication demand and improves the practicability and cost-effectiveness of the system.

[0058] 3. The fixed-time preset performance function is introduced to propose a fault-tolerant control strategy based on fixed time, which improves the stability of the system and ensures the collaboration effect and task reliability of the multi-autonomous body system.

[0059] 4. The adaptive adjustment of the triggering condition reduces the controller update frequency, reduces the system computing burden, and improves the controller response efficiency and system fault tolerance. BRIEF DESCRIPTION OF DRAWINGS

[0060] The drawings accompanying the specification of the present application form a part thereof and serve to provide further understanding of the present application, the illustrative embodiments of the present application and its description serve to explain the present application, and do not constitute an improper limitation of the present application.

[0061] Figure 1 is a communication topology graph between different autonomous bodies provided by one or more embodiments of the present application;

[0062] Figure 2 is a position trajectory graph of the multi-autonomous body system provided by one or more embodiments of the present application;

[0063] Figure 3 is a speed trajectory graph of the multi-autonomous body system provided by one or more embodiments of the present application;

[0064] Figure 4is an interference provided by one or more embodiments of the present application and a corresponding interference observer estimation value;

[0065] Figure 5 is a trigger time graph of an autonomous body provided by one or more embodiments of the present application;

[0066] Figure 6 is a state error response graph of an autonomous body provided by one or more embodiments of the present application. DETAILED DESCRIPTION

[0067] The present application is further described below in conjunction with the accompanying drawings and embodiments.

[0068] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs.

[0069] Term explanation:

[0070] Multi-agent System is a system composed of multiple autonomous agents with certain perception, communication, decision-making and action capabilities. Through local information interaction of each autonomous agent, the state of each autonomous agent is updated and adjusted, and the macro complex global task is completed through mutual cooperation. For example, unmanned aerial vehicle group, robot cooperation and distributed sensor network, etc.

[0071] The following embodiments propose a fixed-time sliding mode control method and system for multi-agent under actuator failure, which combines fixed-time control theory, sliding mode control and event-triggered mechanism. Through this combination, an effective robust cooperative control solution is designed for multi-agent system to achieve fast and reliable tracking performance, which can work effectively even in the face of actuator failure and external disturbance. In addition, through the introduction of the event-triggered mechanism, the present application further reduces the communication demand and improves the practicability and cost-effectiveness of the system.

[0072] Embodiment one:

[0073] The fixed-time sliding mode control method for multi-agent under actuator failure comprises the following steps:

[0074] S1: Constructing the mathematical model of the leader / follower autonomous agent system respectively;

[0075] S2: Determining the network communication topology structure between each autonomous agent in the process of consensus control of multi-agent system;

[0076] S3: Designing a fixed-time disturbance observer;

[0077] S4: Define the consistency state error of the i-th follower autonomous system. Based on the defined consistency error, reconstruct the error model of the multi-autonomous system with a fixed-time preset performance.

[0078] S5: Design of sliding mode surface based on sliding mode control theory. Based on the established sliding mode surface, construct a robust sliding mode control law under actuator failure and unknown external disturbances to compensate for the impact of actuator failure and disturbances on the fault-tolerant control of multi-agent systems;

[0079] S6: Design a dynamic event triggering mechanism for the i-th follower autonomous system to reduce the controller update frequency, thereby reducing the computational burden of the multi-autonomous system.

[0080] S1: Construct a mathematical model of the leader / follower autonomous system.

[0081] The model of the navigator's self-sponsor system is described as follows:

[0082]

[0083] Where p0 and q0 are the states of the navigator, and f0(p0,q0) and u0 represent the nonlinear function and the controller input, respectively.

[0084] The model of a follower-autonomous system is expressed as follows:

[0085]

[0086] Where, p i q i For the state of the follower, f i (p i ,q i ),d i and u i ρ represents the nonlinear function, the unknown external disturbance, and the controller input, respectively; i This indicates the severity of the fault, satisfying 0 < ρ. i <1.

[0087] S2: Determine the network communication topology between the various agents during the consistency and fault tolerance control process of a multi-agent system.

[0088] Using undirected graphs Describe the communication relationships between each agent in the consistency and fault tolerance control process of a multi-agent system. Figure 1 Taking the communication topology diagram between different independent entities as an example, 0 in the diagram is the leader, and 1-4 are all followers.

[0089] in, Let G represent the set of nodes in an undirected graph. Describes the edge set of an undirected graph G. denotes the adjacency matrix of the undirected graph G. The Laplacian matrix where and

[0090] If the i-th follower can receive the information of the j-th leader, then a ij ≠ 0, otherwise, a ij = 0; meanwhile, the communication relationship between the follower and the leader is described by B0= diag{b i0}, if the i-th follower can receive the information of the leader, then b i0 = 1; otherwise, b i0 = 0.

[0091] S3: Design a fixed-time disturbance observer.

[0092] The fixed-time disturbance observer is designed as follows:

[0093]

[0094] where k θ1 is the design parameter, is the estimation of p i , is the estimation of d i , and the estimation error is denoted by Further, we can get:

[0095] S4: Define the consensus state error of the i-th follower multi-agent system, and reconstruct the error model of the multi-agent system with fixed-time preset performance based on the defined consensus error.

[0096] First, define two consensus state errors of the i-th follower agent system as follows:

[0097]

[0098] The preset performance is set as:

[0099]

[0100] where is the fixed-time preset performance function, which is defined as follows:

[0101]

[0102] where l i , and are positive constants satisfying l i > 1, are positive constants.

[0103] The conversion function is defined as where φ(·) is as follows:

[0104]

[0105] where, and c i are positive constants and negative constant, respectively.

[0106] The second-order error of the multi-agent system with fixed time prescribed performance is reconstructed as

[0107]

[0108] where, the results of the conversion function by twice derivation and substituted into each formula are denoted as B i and C i , respectively.

[0109]

[0110]

[0111]

[0112] S5: The designed sliding mode surface is as follows:

[0113]

[0114] where, η 1i > 0, η 2i > 0, k1> 2.

[0115] According to the above linear sliding mode surface, the sliding mode control law and the adaptive law are designed as follows:

[0116]

[0117]

[0118] where, η 3i > 0, η 4i > 0, ξ i > 0, h i > 0, v 3i and μ 2i are design parameters.

[0119] S6: The dynamic event-triggered mechanism can reduce the computational burden of the multi-agent system and the controller update frequency.

[0120] Definition E i (t) = τ i (t) - u i (t) is the measurement error of the controller output, and the event-triggered condition is constructed as follows:

[0121]

[0122] where Ψ i (t) = i i | E i | 2 is the trigger function, i i satisfies i i > 0, and the dynamic variable χ i is set to and 0 < v 1i < 1, v 2i > 0.

[0123] To verify the effectiveness of the scheme, the following simulation experiment begins:

[0124] In the simulation experiment, an event-triggered sliding mode control law based on a fixed-time disturbance observer is designed. This controller can enable the multi-agent system to achieve consistent control in the face of actuator faults and external disturbances. The mathematical models of the leader and follower of the multi-agent system are selected as follows:

[0125] Leader agent system:

[0126]

[0127] where the control input u0 = 1.2sin(t), and the initial state is selected as p0 = 0.5, q0 = 0.1.

[0128] Follower agent system:

[0129]

[0130] where d i = 0.2cos(t), the fault coefficients are set as ρ1 = 0.9, ρ2 = 0.85, ρ3 = 0.95, ρ4 = 0.85, and the initial values are selected as p1 = 0.25, q1 = 0.05, p2 = 0.27, q2 = 0.18, p3 = 0.21, q3 = 0.2, p4 = 0.28, and q4 = 0.3.

[0131] The parameters of the fixed-time disturbance observer k θ1 = 22; the parameters of the preset performance function c = -1, l i = 1.5; the design parameters of the sliding mode function are k1=4, η 1i = 0.1, η 2i = 0.1, η 3i = 2, η 4i = 2.

[0132] Reaching result analysis:

[0133] Select Lyapunov function Taking derivative, we have

[0134] where and According to Lyapunov stability theory, by selecting appropriate parameters, the states of multi-agent system will reach the pre-designed sliding mode surface in fixed time.

[0135] Stability result analysis:

[0136] When the state error of multi-agent system reaches the sliding mode surface, we have Select a Lyapunov function Further, we have According to Lyapunov stability theory and fixed time control theory, eventually all the consistency errors of the agents will converge to zero in fixed time.

[0137] Through Figure 2 and Figure 3 state trajectory curves, we can see that all the states of the agents can eventually achieve consistency stability. According to Fig. 6, the disturbance observer can accurately estimate the size of unknown disturbance in real time. Figure 4 Figure 5 The trigger time of each follower agent system is shown. Figure 6 is the state error response graph of the agent system, which shows that the proposed control algorithm can quickly respond to achieve the control purpose.

[0138] ​In the simulation experiment, the dynamic model of each agent is constructed. By introducing unknown external disturbances and actuator faults, the robustness of the control method can be effectively tested. In addition, an event-triggered mechanism is adopted to reduce communication demand and improve system efficiency. The simulation results are presented in the form of charts, which clearly show the state trajectory, response speed and disturbance observer estimation value of the multi-agent system. These results not only prove that the control method of the present invention can ensure the system to achieve consistent tracking within a fixed time, but also demonstrate its superior performance in dealing with uncertainties and dynamic changes in practical applications. This numerical simulation experiment successfully demonstrates the practicality and efficiency of the control method of the present invention. These simulation results further support the technical advantages of the present invention and provide a strong theoretical basis for future practical applications.

[0139] The present scheme can reduce the controller update frequency, reduce the system computing burden, and improve the controller response efficiency and system stability. The dynamic event-triggered mechanism is adopted, which means that the controller update is not based on fixed time intervals, but on the actual changes in the system controller output. This mechanism can significantly reduce unnecessary control updates, because only when the system controller output changes beyond the preset threshold, the controller needs to be updated. Since the frequency of controller update is reduced, the system computing burden is reduced, which is particularly important for systems with limited computing resources. By reducing unnecessary control updates, the system can run more stably, reducing the potential instability caused by frequent updates.

[0140] The present scheme can enhance the system anti-interference ability and control precision. Sliding mode control is a nonlinear control strategy that can guide the system state to quickly converge to the equilibrium point along the sliding surface after the system state reaches the predetermined sliding surface. By designing a fixed-time disturbance observer, the system can estimate and compensate for unknown external disturbances in real time, thereby improving the robustness of the system. This allows the system to maintain stable operation when facing unknown disturbances, reducing the impact of external factors on system performance. By compensating for disturbances in real time, the system can more accurately control the behavior of the agent, improving the accuracy and reliability of the control.

[0141] The present scheme can improve the system stability, ensure the cooperation effect and task reliability of the multi-agent system. By designing a fixed-time preset performance function, the system can achieve the preset performance requirement within a fixed time regardless of the initial conditions. The present scheme uses a fault-tolerant control strategy to maintain the stability and performance of the system even when the actuator fails. The fixed-time control strategy ensures the rapid convergence of the system state, improving the stability of the system. Even in the case of actuator failure, the system can maintain basic performance and ensure the smooth completion of tasks. In the multi-agent system, each agent can quickly respond and work cooperatively, improving the cooperation effect of the entire system.

[0142] Embodiment two:

[0143] The multi-agent fixed-time sliding mode control system under actuator failure comprises:

[0144] A model construction module is configured to construct models of the leader and follower agent systems according to controller inputs, a nonlinear function, and states of the leader and follower agents.

[0145] A communication relationship module is configured to determine a communication relationship between the follower and the leader according to a network communication topology structure between the agents in a consensus control process of the multi-agent system.

[0146] An interference observer is configured to determine a fixed-time interference observer according to an estimated unknown external interference, a fault severity, and an estimation error.

[0147] An error model is configured to define a consensus state error of an i-th follower agent system according to states of the leader and the follower agents and the communication relationship between the agents, and the consensus state error is within a boundary region of a fixed-time preset performance function constraint, and to reconstruct an error model of the multi-agent system with a fixed-time preset performance according to the defined consensus error.

[0148] A fault-tolerant compensation module is configured to design a sliding mode control law and an adaptive law under actuator failure and unknown external interference based on a set sliding surface, and to compensate for the effects of the actuator failure and the disturbance.

[0149] The above only describes preferred embodiments of the present application and is not intended to limit the present application. Those skilled in the art can make various modifications and changes to the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A fixed-time sliding mode control method for multiple autonomous agents under actuator failures, characterized in that, The method comprises the following steps: According to the controller input, the nonlinear function and the state of the leader and the follower, the model of the leader and the follower autonomous system is constructed respectively; According to the network communication topology structure between each autonomous body in the multi-autonomous body system consistency control process, the communication relationship between the follower and the leader is determined; According to the estimated unknown external disturbance, the fault severity and the estimation error, the fixed time disturbance observer is determined; A consensus state error of the first follower autonomous system is defined according to the states of the leader and the followers and the communication relationship between the autonomous systems, and the consensus state error is in a boundary region of a fixed-time pre-set performance function constraint. i A consensus state error of the first follower autonomous system is defined according to the states of the leader and the followers and the communication relationship between the autonomous systems, and the consensus state error is in a boundary region of a fixed-time pre-set performance function constraint. According to the defined consistency state error, the error model of the multi-autonomous body system with fixed time preset performance is reconstructed; Based on the set sliding surface, the sliding mode control law and the adaptive law under the actuator fault and the unknown external disturbance are designed to compensate the influence of the actuator fault and the disturbance.

2. The fixed-time sliding mode control method for multiple agents under actuator faults as claimed in claim 1, wherein, Also has dynamic event triggering mechanism, specifically: set the first i The dynamic event triggering mechanism of the follower autonomous system, define The measurement error output by the controller, construct event trigger condition as follows: wherein is a trigger function, satisfies , is an actual control signal, is a controller output signal, is a trigger sequence of control signals, dynamic variable χ i is set to 3. The method of claim 2, wherein The model of the leader and the follower autonomous system is as follows: The model of the leader autonomous system is as follows: wherein, p 0, q 0 is a state of the pilot, f 0( p 0, q 0), u 0 respectively denote a non-linear function and a controller input; The model of the follower autonomous system is as follows: wherein p i , q i is the state of the follower, f i p i , q i , d i and u i denote a nonlinear function, an unknown external disturbance and a controller input, respectively; According to the network communication topology structure between each autonomous body in the multi-autonomous body system consistency control process, the communication relationship between the follower and the leader is determined, and the fixed time disturbance observer is as follows: i denotes the severity of the fault, satisfying 0 The consistency state error is in the boundary region of the fixed time preset performance function constraint, and the fixed time disturbance observer is as follows: i <1.​ 4. The method of claim 3, wherein Based on the set sliding surface, the sliding mode control law and the adaptive law under the actuator fault and the unknown external disturbance are designed, and the sliding mode control law and the adaptive law are as follows: Utilizing undirected graphs Describing the communication relationship between each autonomous body in the consistent fault-tolerant control process of the multi-autonomous body system; wherein denotes a set of nodes of the undirected graph G, denotes a set of edges of the undirected graph G, denotes an adjacency matrix of the undirected graph G; Laplacian matrix wherein and If the ego i is able to receive information from the ego j , then a ij ≠ 0, otherwise, a ij = 0; with B 0 = diag{ b i0} describing the communication relation between the followers and the leader, if the i first follower ego is able to receive information from the leader, then b i0 = 1; otherwise, b i0 = 0.

5. The method of claim 4, wherein, The sliding mode control law and the adaptive law are as follows: where k θ1 is a design parameter, is an estimate of The method comprises the following steps: i The model construction module is configured to construct the model of the leader and the follower autonomous system according to the controller input, the nonlinear function and the state of the leader and the follower; i is a severity of the fault, is an estimate of d i d i is an unknown external disturbance, q i is a state of the follower, u i is a controller input, and the estimation error is denoted by​​ 6. The fixed-time sliding mode control method for multiple agents under actuator faults of claim 5, wherein, Based on the states of the leader and the followers and the communication relations between the individual agents, the consistency state error of the follower agent system is defined as follows: i Econsist = (1 - a) * Econsist + a * (Eleader - Efollower) ； wherein, p 0 、q 0 is the state of the leader, p i 、q i 、p j 、q j is the state of the follower, if the follower autonomous body i is able to receive information from the autonomous body j , b i = 1, otherwise, b i =0。 7. The fixed-time sliding mode control method for multiple agents under actuator faults of claim 6, wherein, The communication relationship module is configured to determine the communication relationship between the follower and the leader according to the network communication topology structure between each autonomous body in the multi-autonomous body system consistency control process; The preset performance is set as: wherein, is a fixed time preset performance function, is a lower bound parameter for the function, is an upper bound parameter for the function, as follows: wherein l i ， ， and is a positive number satisfying l i >1, >0, >

0.

8. The fixed-time sliding mode control method for multiple agents under actuator faults of claim 7, wherein, According to the definition of the consistent state error, the error model of the multi-agent system with fixed time preset performance is reconstructed, specifically: the second order error of the multi-agent system with fixed time preset performance is reconstructed to obtain ; wherein the conversion function is defined as , wherein , B i is the acceleration of the system, C i is the acceleration coefficient.

9. The method of claim 8, wherein, The disturbance observer is configured to determine the fixed time disturbance observer according to the estimated unknown external disturbance, the fault severity and the estimation error; The set sliding surface is as shown in the following formula: ; wherein ; The fault tolerant compensation module is configured to design the sliding mode control law and the adaptive law under the actuator fault and the unknown external disturbance based on the set sliding surface, and compensate the influence of the actuator fault and the disturbance. wherein , , v 3i and ​ 2i is a design parameter, β is a controller parameter.

10. A fixed time sliding mode control system for multiple autonomous agents under actuator failures, characterized in that, ​ ​ ​ ​ An error model is configured to define a consensus state error of the first follower autonomous system according to states of the leader and the follower and a communication relationship between the respective autonomous bodies, the consensus state error being in a boundary region of a fixed-time preset performance function constraint, and the error model of the multi-autonomous body system with the fixed-time preset performance is reconstructed according to the defined consensus state error. i An error model is configured to define a consensus state error of the first follower autonomous system according to states of the leader and the follower and a communication relationship between the respective autonomous bodies, the consensus state error being in a boundary region of a fixed-time preset performance function constraint, and the error model of the multi-autonomous body system with the fixed-time preset performance is reconstructed according to the defined consensus state error. ​

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