Multi-agent fixed time sliding mode control method and system under actuator fault

Abstract

The invention relates to a fixed-time sliding-mode control method and system for multiple self-subjects under an actuator fault. The method comprises the following steps: respectively constructing models of a navigator self-subject system and a follower self-subject system; according to a network communication topological structure among the self-agents in the consistency control process of the multi-self-agent system, determining a communication relationship between the follower and the navigator; determining a fixed time interference observer according to the estimated unknown external interference, the fault severity and the estimation error; according to the states of the navigator and the followers and the communication relation between the self-subjects, the consistency state error of the ith follower self-subject system is defined, the consistency state error is located in a boundary area constrained by a preset performance function in fixed time, and a multi-self-subject system error model is reconstructed according to the consistency error; and based on the set sliding mode surface, designing a sliding mode control law and an adaptive law under the actuator fault and unknown external interference, and compensating the influence of the actuator fault and disturbance.

Description

Technical Field

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

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

[0003] A multi-agent system is a system composed of multiple agents with certain perception, communication, decision-making and action capabilities. Each agent updates and adjusts its own state through local information interaction, and cooperates with each other to complete macro-complex global tasks. These systems include but are not limited to drone swarms, robot collaboration, and distributed sensor networks. Multi-agent systems have received 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 consistency control strategy, which ensures that all agents can work together to achieve a common goal.

[0004] However, traditional control methods have some inherent limitations when dealing with the collaborative control of multi-agent systems.

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

[0006] Secondly, disturbances in actual applications and actuator uncertainties or failures may seriously affect the control performance and even cause system instability.

[0007] In addition, many systems require real-time or near real-time performance, which requires that the control strategy must be able to ensure the convergence of the system state within a predetermined strict time.

[0008] To overcome these problems, fixed-time control strategies can ensure that the system reaches a stable state 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 attractive in theory, applying them 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 exchange with limited communication resources. Summary of the invention

[0009] In order to solve the technical problems existing in the above background technology, the present invention provides a fixed-time sliding mode control method and system for multiple autonomous agents under actuator failure, which combines fixed-time control theory, sliding mode control and event triggering mechanism to design an effective robust cooperative control solution for multiple autonomous agent systems to achieve fast and reliable tracking performance, which can work effectively even in the face of actuator failure and external interference. In addition, by introducing the event triggering mechanism, the communication requirements are further reduced, and the practicality and cost-effectiveness of the system are improved.

[0010] In order to achieve the above object, the present invention adopts the following technical solution:

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

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

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

[0014] Determine a fixed-time disturbance observer according to the estimated unknown external disturbance, the fault severity and the estimation error;

[0015] According to the states of the leader and the follower and the communication relationship between the autonomous agents, the consistency state error of the i-th follower autonomous agent system is defined, and the consistency state error is within the boundary area constrained by the fixed time preset performance function; according to the defined consistency error, the error model of the multi-agent system with fixed time preset performance is reconstructed;

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

[0017] Furthermore, there is also a dynamic event triggering mechanism, specifically: setting the dynamic event triggering mechanism of the i-th follower autonomous system, defining E i (t) = τ i (t)-u i (t) is the measurement error output by the controller, and the event triggering conditions are constructed as follows:

[0018]

[0019] Among them, i (t) = ι i |E i | 2is the trigger function, ι i Satisfaction i >0, dynamic variable χ i Set as and 0 <v 1i <1, v 2i >0.

[0020] Furthermore, the model of the leader and follower autonomous system is as follows;

[0021] The model of the navigator autonomous system is shown below:

[0022]

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

[0024] The model of the follower autonomous system is shown below:

[0025]

[0026] Among them, p i ,q i is the state of the follower, f i (p i ,q i ), d i and u i Respectively represent nonlinear function, unknown external disturbance and controller input; ρ i Indicates the severity of the fault, satisfying 0<ρ i <1.

[0027] Furthermore, according to the network communication topology between each autonomous agent in the consistency control process of the multi-agent system, the communication relationship between the follower and the leader is determined; specifically:

[0028] Using undirected graphs Describe the communication relationship between each autonomous agent in the process of consistent fault-tolerant control of multi-agent systems;

[0029] in, represents the set of nodes of the undirected graph G, represents the edge set of the undirected graph G, Represents the adjacency matrix of the undirected graph G; Laplacian matrix in and

[0030] If agent i can receive information from agent j, then a ij ≠0, otherwise, aij =0; B0 = diag{b i0} describes the communication relationship between the follower and the navigator. If the i-th follower agent can receive the information from the navigator, then b i0 =1; otherwise, b i0 =0.

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

[0032]

[0033] Among them, k θ1 is the design parameter, is the right i Estimate of ρ i is the severity of the fault, Yes i The estimate of i is the unknown external disturbance, and the estimated error is recorded as

[0034] Furthermore, according to the states of the leader and the follower and the communication relationship between the autonomous agents, the consistency state error of the i-th follower autonomous agent system is defined as shown in the following formula:

[0035]

[0036] Among them, p0 and q0 are the states of the navigator, p i ,q i 、p j ,q j is the state of the follower. If the follower agent i can receive the information of agent j, then b i =1, otherwise, b i =0.

[0037] Furthermore, the consistency state error is within the boundary region constrained by a fixed time preset performance function, specifically:

[0038] The default performance settings are:

[0039] in, The performance function is preset for a fixed time, as shown below:

[0040]

[0041] Among them, l i , and Is to satisfy l i >1, A normal number.

[0042] Furthermore, according to the defined consistency 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: The conversion function is defined as in

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

[0044] The set sliding surface is shown as follows: Among them, η 1i >0,η 2i >0, k1>2;

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

[0046]

[0047]

[0048] Among them, η 3i >0,η 4i >0,ξ i >0,h i >0, v 3i and μ 2i is the design parameter.

[0049] A second aspect of the present invention provides a fixed-time sliding mode control system of multiple autonomous agents under actuator failure, including.

[0050] The model building module is configured to: build models of the leader and follower autonomous systems respectively according to the controller input, the nonlinear function, and the states of the leader and the follower;

[0051] 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 the autonomous agents in the consistency control process of the multi-agent system;

[0052] The disturbance observer is configured to: determine a fixed-time disturbance observer based on the estimated unknown external disturbance, the fault severity, and the estimation error;

[0053] The error model is configured to: define the consistency state error of the i-th follower autonomous system according to the states of the leader and the follower and the communication relationship between the autonomous agents, the consistency state error is within the boundary region constrained by the fixed-time preset performance function, and reconstruct the error model of the multi-autonomous system with the fixed-time preset performance according to the defined consistency error;

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

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

[0056] 1. Combining fixed-time control theory and sliding mode control, an effective robust collaborative control solution is designed for multi-agent systems, which can cope with uncertainty and external interference, enhance the system's anti-interference ability and control accuracy, ensure smooth and accurate control, and achieve fast and reliable tracking performance, even in the face of actuator failures and external interference.

[0057] 2. Through the introduction of event triggering mechanism, the communication requirements are further reduced, and the practicality and cost-effectiveness of the system are improved.

[0058] 3. By introducing a fixed-time preset performance function, a fixed-time-based fault-tolerant control strategy is proposed to improve system stability and ensure the collaborative effect and task reliability of the multi-autonomous system.

[0059] 4. By adaptively adjusting the trigger conditions, the controller update frequency is reduced, the system calculation burden is reduced, and the controller response efficiency and system fault tolerance are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0061] Figure 1 is a communication topology diagram between different autonomous entities provided by one or more embodiments of the present invention;

[0062] Figure 2 is a position trajectory diagram of a multi-agent system provided by one or more embodiments of the present invention;

[0063] Figure 3 is a velocity trajectory diagram of a multi-agent system provided by one or more embodiments of the present invention;

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

[0065] Figure 5 is a triggering timing diagram of an autonomous body provided by one or more embodiments of the present invention;

[0066] Figure 6 It is a state error response diagram of an autonomous subject provided by one or more embodiments of the present invention. DETAILED DESCRIPTION

[0067] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0068] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0069] Terminology explanation:

[0070] A multi-agent system is a system composed of multiple agents with certain perception, communication, decision-making and action capabilities. Each agent updates and adjusts its own state through local information interaction, and collaborates with each other to complete macro-complex global tasks. Examples include drone swarms, robot collaboration, and distributed sensor networks.

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

[0072] Embodiment 1:

[0073] The fixed-time sliding mode control method for multiple autonomous agents under actuator failure includes the following steps:

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

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

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

[0077] S4: define the consistency state error of the i-th follower autonomous system, and reconstruct the multi-agent system error model with fixed time preset performance based on the defined consistency error;

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

[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-agent system.

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

[0081] The model of the navigator autonomous system is expressed as:

[0082]

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

[0084] The model of the follower autonomous system is expressed as:

[0085]

[0086] Among them, p i ,q i is the state of the follower, f i (p i ,q i ), d i and u i Respectively represent nonlinear function, unknown external disturbance and controller input; ρ i Indicates the severity of the fault, satisfying 0<ρ i <1.

[0087] S2: Determine the network communication topology between each autonomous agent in the process of consistent fault-tolerant control of the multi-autonomous agent system.

[0088] Using undirected graphs Describe the communication relationship between each autonomous agent in the process of consistent fault-tolerant control of multi-agent system. Figure 1 Take the communication topology diagram between different autonomous entities shown as an example, where 0 is the leader and 1-4 are followers.

[0089] in, represents the set of nodes of the undirected graph G, represents the edge set of the undirected graph G, Represents the adjacency matrix of the undirected graph G. Laplacian matrix in and

[0090] If agent i can receive information from agent j, then a ij ≠0, otherwise, a ij =0; at the same time, use B0=diag{b i0} to describe the communication relationship between the follower and the navigator. If the i-th follower agent can receive the information of the navigator, 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] Among them, k θ1 is the design parameter, is the right i The estimate, Yes i The estimation error is recorded as Then we can get:

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

[0096] First, the two consistency state errors of the i-th follower autonomous system are defined as:

[0097]

[0098] The default performance settings are:

[0099]

[0100] in, The performance function is preset for a fixed time and is defined as follows:

[0101]

[0102] Among them, l i , and Is to satisfy l i >1, A normal number.

[0103] The conversion function is defined as in The form of φ(·) is as follows:

[0104]

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

[0106] The second-order error of the multi-agent system with fixed time preset performance is reconstructed to obtain:

[0107]

[0108] Among them, the results obtained by taking the second derivative of the transfer function and substituting it into each formula are recorded as B i and C i .

[0109]

[0110]

[0111]

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

[0113]

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

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

[0116]

[0117]

[0118] Among them, η 3i >0,η 4i >0,ξ i >0,h i >0, v 3i and μ 2i is the design parameter.

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

[0120] Definition E i (t) = τ i (t)-u i (t) is the measurement error output by the controller, and the event triggering conditions are constructed as follows:

[0121]

[0122] Among them, i (t) = ι i |E i | 2 is the trigger function, ι i Satisfaction i >0, dynamic variable χ i Set as and 0 <v 1i <1, v 2i >0.

[0123] In order to verify the effectiveness of this solution, the simulation experiment is started as follows:

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

[0125] Navigator autonomous system:

[0126]

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

[0128] Follower Autonomous System:

[0129]

[0130] Among them, d i =0.2cos(t), the fault coefficient is set to 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, q4=0.3 respectively.

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

[0132] Analysis of reachability results:

[0133] Select the Lyapunov function The derivative can be obtained

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

[0135] Stability results analysis:

[0136] When the state error of the multi-agent system reaches the sliding surface, we can get Choose a Lyapunov function Further According to Lyapunov stability theory and fixed-time control theory, the consistency errors of all autonomous bodies will eventually converge to zero within a fixed time.

[0137] pass Figure 2 and Figure 3 The state trajectory curve shows that all autonomous states can eventually achieve consistent stability. Figure 4 As shown, the disturbance observer can accurately estimate the size of unknown disturbance in real time. Figure 5 The triggering moment of each follower's autonomous system is shown. Figure 6 It is the state error response diagram of the autonomous system, which shows that the proposed control algorithm can respond quickly to achieve the control purpose.

[0138] In the simulation experiment, a dynamic model of each autonomous agent was constructed. By introducing unknown external disturbances and actuator failures, the robustness of the control method can be effectively tested. In addition, an event triggering mechanism is adopted to reduce communication requirements and improve system efficiency. The simulation results are presented in the form of charts, which clearly show the state trajectory, response speed and estimated value of the disturbance observer of the multi-agent system. These results not only prove that the control method of the present invention can ensure that the system can achieve consistent tracking within a fixed time, but also show its superior performance in dealing with uncertainties and dynamic changes in practical applications. This numerical simulation experiment successfully demonstrated 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] This solution can reduce the frequency of controller updates, reduce the system computational burden, and improve controller response efficiency and system stability. A dynamic event trigger mechanism is used, which means that the controller update is not based on a fixed time interval, but on the actual change of the system controller output. This mechanism can significantly reduce unnecessary control updates because the controller only needs to be updated when the system controller output changes by more than a preset threshold. Since the controller update frequency is reduced, the computational burden of the system is reduced, which is particularly important for systems with limited computing resources. By reducing unnecessary control updates, the system can run more stably and reduce the potential instability caused by frequent updates.

[0140] This solution can enhance the system's anti-interference ability and control accuracy. Sliding mode control is a nonlinear control strategy that can guide the system state to converge quickly 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 enables the system to maintain stable operation in the face of 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 autonomous subject, improving the accuracy and reliability of control.

[0141] This solution can improve system stability and ensure the collaborative effect and task reliability of the multi-agent system. By designing a fixed-time preset performance function, the system can achieve the preset performance requirements within a fixed time, regardless of the initial conditions. Through the fault-tolerant control strategy, this solution can maintain the stability and performance of the system when the actuator fails. The fixed-time control strategy ensures the rapid convergence of the system state and improves the stability of the system. Even in the event of an actuator failure, the system can maintain basic performance and ensure the smooth completion of the task. In a multi-agent system, each agent can respond quickly and work together, improving the collaborative effect of the entire system.

[0142] Embodiment 2:

[0143] Fixed-time sliding mode control system for multiple autonomous agents under actuator failure, including:

[0144] The model building module is configured to: build models of the leader and follower autonomous systems respectively according to the controller input, the nonlinear function, and the states of the leader and the follower;

[0145] 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 the autonomous agents in the consistency control process of the multi-agent system;

[0146] The disturbance observer is configured to: determine a fixed-time disturbance observer based on the estimated unknown external disturbance, the fault severity, and the estimation error;

[0147] The error model is configured to: define the consistency state error of the i-th follower autonomous system according to the states of the leader and the follower and the communication relationship between the autonomous agents, the consistency state error is within the boundary region constrained by the fixed-time preset performance function, and reconstruct the error model of the multi-autonomous system with the fixed-time preset performance according to the defined consistency error;

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

[0149] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

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

2. The fixed-time sliding mode control method for multiple agents under actuator failure as claimed in claim 1, characterized in that: It also has a dynamic event triggering mechanism, specifically: set the dynamic event triggering mechanism of the i-th follower autonomous system, define E i (t) = τ i (t)-u i (t) is the measurement error output by the controller, and the event triggering conditions are constructed as follows: Among them, i (t) = l i |E i |2 is the trigger function, ι i Satisfaction i >0, dynamic variable χ i Set as And 0<ν 1i <1, ν 2i >0.

3. The fixed-time sliding mode control method for multiple agents under actuator failure as claimed in claim 1, characterized in that: The model of the leader and follower autonomous system is as follows: The model of the navigator autonomous system is shown below: Among them, p0 and q0 are the states of the navigator, f0(p0,q0) and u0 represent the nonlinear function and controller input respectively; The model of the follower autonomous system is shown below: Among them, p i ,q i is the state of the follower, f i (p i ,q i ), d i and u i Respectively represent nonlinear function, unknown external disturbance and controller input; ρ i Indicates the severity of the fault, satisfying 0<ρ i <1.

4. The fixed-time sliding mode control method for multiple agents under actuator failure as claimed in claim 1, characterized in that: According to the network communication topology between each autonomous agent in the consistency control process of the multi-agent system, the communication relationship between the follower and the leader is determined; specifically: Using undirected graphs Describe the communication relationship between each autonomous agent in the process of consistent fault-tolerant control of multi-agent systems; in, represents the set of nodes of the undirected graph G, represents the edge set of the undirected graph G, Represents the adjacency matrix of the undirected graph G; Laplacian matrix in and If agent i can receive information from agent j, then a ij ≠0, otherwise, a ij =0; using B0 = diag{b i0 } describes the communication relationship between the follower and the navigator. If the i-th follower agent can receive the information from the navigator, then b i0 =1; otherwise, b i0 =0.

5. The fixed-time sliding mode control method for multiple agents under actuator failure as claimed in claim 1, characterized in that: The fixed-time disturbance observer is shown in the following equation: Among them, k θ1 is the design parameter, is the right i Estimate of ρ i is the severity of the fault, Yes i The estimate of i is the unknown external disturbance, and the estimated error is recorded as 6. The fixed-time sliding mode control method for multiple agents under actuator failure as claimed in claim 1, characterized in that: According to the states of the leader and the follower and the communication relationship between the autonomous agents, the consistency state error of the i-th follower autonomous agent system is defined as shown in the following formula: Among them, p0 and q0 are the states of the navigator, p i ,q i 、p j ,q j is the state of the follower. If the follower agent i can receive the information of agent j, then b i =1, otherwise, b i =0.

7. The fixed-time sliding mode control method for multiple agents under actuator failure as claimed in claim 1, characterized in that: The consistency state error is within the boundary area constrained by the fixed time preset performance function, specifically: The default performance settings are: in, The performance function is preset for a fixed time, as shown below: Among them, l i , and Is to satisfy l i >1, A normal number.

8. The fixed-time sliding mode control method for multiple agents under actuator failure as claimed in claim 1, characterized in that: According to the defined consistency 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: The conversion function is defined as in 9. The fixed-time sliding mode control method for multiple agents under actuator failure as claimed in claim 1, characterized in that: Based on the set sliding surface, the sliding mode control law and adaptive law are designed under actuator failure and unknown external disturbance, as shown in the following formula: The set sliding surface is shown as follows: Among them, η 1i >0,η 2i >0, k1>2; The sliding mode control law and adaptive law are shown in the following equations: Among them, η 3i >0,η 4i >0,ξ i >0,h i >0, ν 3i and μ 2i is the design parameter.

10. A fixed-time sliding mode control system for multiple agents under actuator failure, characterized in that: include: The model building module is configured to: build models of the leader and follower autonomous systems respectively according to the controller input, the nonlinear function, and the states of the leader and the follower; 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 the autonomous agents in the consistency control process of the multi-agent system; The disturbance observer is configured to: determine a fixed-time disturbance observer based on the estimated unknown external disturbance, the fault severity, and the estimation error; The error model is configured as follows: according to the states of the leader and the follower and the communication relationship between the autonomous agents, a consistency state error of the i-th follower autonomous agent system is defined, the consistency state error is within the boundary region constrained by the fixed time preset performance function, and according to the defined consistency error, the error model of the multi-autonomous agent system with the fixed time preset performance is reconstructed; The fault-tolerant compensation module is configured to: design a sliding mode control law and an adaptive law under actuator failure and unknown external disturbance based on a set sliding surface, and compensate for the influence of actuator failure and disturbance.

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