A Control Method and Device for a Multi-Agent System Oriented to the Water Surface

Abstract

The present application relates to a control method and device for a multi-agent system on the water surface, belonging to the technical field of ship autonomous driving. Among them, the method includes: taking the position and speed information of the agents as state variables to construct a mathematical model of the multi-agent system on the water surface; according to the universal approximation principle of the fuzzy logic system, approximating the non-linear functions in the mathematical model to construct a fuzzy state observer for estimating the unmeasurable states in the mathematical model; determining the generalized state error introduced with a time-varying formation function, and calculating the target control input according to the sliding mode control algorithm. The present application accurately estimates the unmeasurable information in the multi-agent system on the water surface through the fuzzy state observer, reduces the dependence of the controller on the single-ship speed state information, improves the control accuracy, and at the same time combines the time-varying formation function with the sliding mode control algorithm, enabling the formation of the multi-agent system on the water surface to change with time, and this time-varying formation has higher flexibility.

Description

Technical Field

[0001] This application relates to the technical field of ship autonomous driving, and particularly to a control method and device for a multi-agent system on the water surface. Background Art

[0002] Ship motion has characteristics such as large time delay, large inertia, and non-linearity. Changes in ship speed and loading lead to parameter perturbation problems in the control model. Changes in navigation conditions, interference from environmental parameters, and inaccurate measurements all make the ship heading control system uncertain. In the face of the problems brought by these non-linear uncertainties, intelligent algorithms have emerged and have been continuously applied to the field of ship heading control, such as adaptive control, robust control, fuzzy adaptive control, iterative sliding mode control, least parameter learning method, etc.

[0003] In the prior art, state feedback control methods are often used in the design of multi-agent systems on the water surface, and this method is based on the known full state information of the multi-agent system on the water surface.

[0004] However, due to physical limitations of sensors, measurement early birth, etc., in actual navigation, the single-ship speed state information in the multi-agent system cannot be measured in real time, resulting in the inability to transmit accurate speed state information to the controller for updating control signals, resulting in poor control accuracy of the multi-agent system on the water surface. Summary of the Invention

[0005] In view of this, it is necessary to provide a control method and device for a multi-agent system on the water surface to solve the problem of poor control accuracy existing in the prior art.

[0006] To solve the above problems, this application provides a control method for a multi-agent system on the water surface, including:

[0007] Taking the position and speed information of the agent as state variables, constructing an initial mathematical model of the multi-agent system on the water surface;

[0008] According to the universal approximation principle of the fuzzy logic system, approximating the non-linear function in the initial mathematical model to obtain a target mathematical model;

[0009] According to the input and output of the target mathematical model, constructing a fuzzy state observer for estimating the unmeasurable state in the target mathematical model;

[0010] Based on the target mathematical model and the fuzzy state observer, determining a generalized state error introduced with a time-varying formation function;

[0011] According to the sliding mode control algorithm, calculating the target control input of the multi-agent system on the water surface based on the generalized state error.

[0012] In some possible implementation manners, the initial mathematical model is as follows:

[0013]

[0014]

[0015] In the formula, represents the position state information of the -th agent in the multi-agent system on the water surface, represents the velocity state information of the -th agent in the multi-agent system on the water surface, represents the external disturbance received by the -th agent in the multi-agent system on the water surface, represents the target control input of the -th agent in the multi-agent system on the water surface, represents a nonlinear function;

[0016] The target mathematical model is as follows:

[0017]

[0018]

[0019] In the formula, represents the optimal weight matrix of the -th agent in the multi-agent system on the water surface, represents the fuzzy basis function of the -th agent in the multi-agent system on the water surface, represents the estimated velocity state information of the -th agent in the multi-agent system on the water surface, represents the fuzzy minimum approximation error of the -th agent in the multi-agent system on the water surface, represents the approximation error of the -th agent in the multi-agent system on the water surface.

[0020] In some possible implementation manners, the fuzzy state observer is as follows:

[0021]

[0022]

[0023] In the formula, represents the estimated position state information of the -th agent in the multi-agent system on the water surface, represents the estimated position state information of the The speed state information of each agent, Represents the estimated The weight matrix of each agent, and Represents a constant.

[0024] In some possible implementations, the generalized state error is:

[0025]

[0026]

[0027]

[0028]

[0029] In the formula, Represents the first The generalized state error of an agent, represents the time-varying formation function used to adjust the formation of the surface multi-agent system, Represents the first The agent and The quality of communication between agents, Represents the first The weighted value of the communication quality between an agent and all other agents, is an adjacency matrix, when When the leader is represented, Change to .

[0030] In some possible implementations, according to a sliding mode control algorithm, a target control input of the surface multi-agent system is obtained based on the generalized state error calculation, including:

[0031] Based on the generalized state error, determining a time-varying sliding mode variable;

[0032] Determining a time-varying sliding mode surface based on the time-varying sliding mode variable;

[0033] Based on the time-varying sliding surface, a target control input is calculated.

[0034] In some possible implementations, the time-varying sliding mode variables include time-varying terminal sliding mode variables and time-varying linear auxiliary sliding mode variables, the time-varying sliding mode surface includes a time-varying terminal sliding mode surface and a time-varying linear auxiliary sliding mode surface, and the time-varying linear auxiliary sliding mode surface is used to switch from the time-varying terminal sliding mode surface to the time-varying linear auxiliary sliding mode surface when encountering a singularity problem.

[0035] In some possible implementation manners, the time-varying terminal sliding mode variable and the time-varying linear auxiliary sliding mode variable are respectively:

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] wherein, represents the time-varying terminal sliding mode variable of the -th agent in the water surface multi-agent system, represents the time-varying linear auxiliary sliding mode variable of the -th agent in the water surface multi-agent system, represents the generalized state error of the -th agent in the water surface multi-agent system, represents a positive constant, represents a constant, represents a matrix with diagonal elements of , and , represents a matrix with diagonal elements of , and , represents the sign function, , and represent the first, second, and third components of the generalized state error of the -th agent in the water surface multi-agent system.

[0042] In some possible implementation manners, based on the time-varying sliding mode surface, calculating a target control input includes:

[0043] Calculating an initial control input based on the time-varying sliding mode surface;

[0044] Calculating a target control input considering actuator saturation based on the initial control input.

[0045] In some possible implementation manners, the method further includes: determining an actual control input based on the target control input, and the actual control input is:

[0046]

[0047]

[0048]

[0049] In the formula, represents the actual control input at time represents the target control input at time represents the measurement error of the control input, represents the target control input at time and represents a positive integer.

[0050] The present application also provides an output feedback control device for a surface multi-agent system, including:

[0051] A model construction unit, configured to construct an initial mathematical model of the surface multi-agent system by using the position and velocity information of the agents as state variables;

[0052] A fuzzy observation unit, configured to approximate the non-linear function in the initial mathematical model according to the universal approximation principle of the fuzzy logic system to obtain a target mathematical model, and construct a fuzzy state observer for estimating the unmeasurable state in the target mathematical model according to the input and output of the target mathematical model;

[0053] A sliding mode control unit, configured to determine a generalized state error introducing a time-varying formation function based on the target mathematical model and the fuzzy state observer, and calculate the target control input of the surface multi-agent system based on the generalized state error according to the sliding mode control algorithm.

[0054] The beneficial effects of the present application are as follows: The control method for the surface multi-agent system provided by the present application uses a fuzzy state observer to accurately estimate the unmeasurable information in the surface multi-agent system, solves the output feedback problem of the multi-agent system, effectively reduces the dependence of the controller on the single-ship speed state information, and while solving problems such as model uncertainty, unknown speed state information, input saturation, and uncertain external interference in the multi-agent system, effectively improves the control accuracy.

[0055] Furthermore, the present application combines a time-varying formation function with a sliding mode control method, and proposes a new type of time-varying sliding mode control method, so that the formation of the surface multi-agent system can change with time, and the flexibility of this time-varying formation is improved compared with the traditional time-invariant formation. Brief Description of the Drawings

[0056] Figure 1A schematic flowchart of an embodiment of the control method for a multi-agent system facing the water surface provided by this application;

[0057] Figure 2 For this application Figure 1 A schematic flowchart of an embodiment of step S105 in it;

[0058] Figure 3 For this application Figure 2 A schematic flowchart of an embodiment of step S203 in it;

[0059] Figure 4 A schematic structural diagram of an embodiment of the output feedback control device for the multi-agent system facing the water surface provided by this application. Detailed implementation manners

[0060] Next, the technical solutions in the embodiments of this application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are only a part of the embodiments of this application, rather than all the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of this application.

[0061] It should be understood that the schematic drawings are not drawn to scale. The flowcharts used in this application illustrate the operations implemented according to some embodiments of this application. It should be understood that the operations in the flowcharts may not be implemented in sequence, and steps without logical context relationships may be reversed or implemented simultaneously. In addition, those skilled in the art can add one or more other operations to the flowchart or remove one or more operations from the flowchart under the guidance of the content of this application. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor systems and / or microcontroller systems.

[0062] The descriptions such as "first" and "second" involved in the embodiments of this application are only for the purpose of implicit description and cannot be understood as indicating or implying their relative importance or implicitly specifying the quantity of the indicated technical features. Therefore, the technical features defined with "first" and "second" may explicitly or implicitly include at least one such feature. "And / or" describes the association relationship of associated objects and indicates that three relationships may exist. For example: A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone, these three situations.

[0063] References to "embodiments" in this specification mean that specific features, structures, or characteristics described in connection with the embodiments can be included in at least one embodiment of the present application. The phrase appears in various places in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0064] The present application provides a control method for a surface multi-agent system, which will be described separately below.

[0065] Figure 1 It is a schematic flowchart of an embodiment of the control method for a surface multi-agent system provided by the present application. As Figure 1 shown, the control method for a surface multi-agent system includes:

[0066] S101. Using the position and speed information of the agent as state variables, construct an initial mathematical model of the surface multi-agent system;

[0067] In a specific embodiment, using the collected single-ship information and considering the non-linear characteristics of the surface multi-agent, the initial mathematical model of the surface multi-agent system is constructed as:

[0068]

[0069]

[0070] In the formula, represents the position state information of the surface agent, represents the transformation matrix for converting the ship body coordinate system to the earth coordinate system, represents the speed state information of the surface agent in the ship body coordinate system, represents the inertia matrix of the surface agent, represents the Coriolis centripetal force matrix of the surface agent, represents the damping matrix of the surface agent, represents the external disturbance received by the surface agent, represents the control input of the surface agent.

[0071] Let , the above initial mathematical model becomes:

[0072]

[0073]

[0074] In the formula, represents the speed state information of the surface agent in the earth coordinate system, Denote the Coriolis centripetal force matrix of the water surface agent, Denote the damping matrix of the water surface agent, Denote the external disturbance received by the water surface agent, Denote the control input of the water surface agent.

[0075] Let again , and the final initial mathematical model is obtained as:

[0076]

[0077]

[0078] In the formula, Denote the position state information of the th agent in the multi-agent system on the water surface, Denote the velocity state information of the th agent in the multi-agent system on the water surface, Denote the external disturbance received by the th agent in the multi-agent system on the water surface, Denote the target control input of the th agent in the multi-agent system on the water surface, Denote the nonlinear function, where the velocity state information is unmeasurable information.

[0079] S102. According to the universal approximation principle of the fuzzy logic system, approximate the nonlinear function in the initial mathematical model to obtain the target mathematical model;

[0080] In a specific embodiment, it includes:

[0081] First, define the ideal parameter vector of the multi-agent system on the water surface as:

[0082]

[0083] In the formula, Denote compact set of, Denote compact set of.

[0084] Then, according to the above ideal parameter vector, the fuzzy minimum approximation error is:

[0085]

[0086] Next, according to the universal approximation principle of the fuzzy logic system, the nonlinear function can be approximated by the fuzzy logic system as:

[0087]

[0088] In the formula, represents the optimal weight matrix of the th agent in the surface multi-agent system, represents the fuzzy basis function of the th agent in the surface multi-agent system, represents the approximation error of the th agent in the surface multi-agent system.

[0089] Substituting the above formula into the initial mathematical model, the target mathematical model is obtained as:

[0090]

[0091]

[0092] In the formula, represents the position state information of the th agent in the surface multi-agent system, represents the velocity state information of the th agent in the surface multi-agent system, represents the external disturbance received by the th agent in the surface multi-agent system, represents the target control input of the th agent in the surface multi-agent system, represents the optimal weight matrix of the th agent in the surface multi-agent system, represents the fuzzy basis function of the th agent in the surface multi-agent system, represents the estimated velocity state information of the th agent in the surface multi-agent system, represents the fuzzy minimum approximation error of the th agent in the surface multi-agent system, represents the approximation error of the th agent in the surface multi-agent system.

[0093] S103. According to the input and output of the target mathematical model, construct a fuzzy state observer for estimating the unmeasurable state in the target mathematical model;

[0094] In a specific embodiment, the designed fuzzy state observer is:

[0095]

[0096]

[0097] In the formula, represents the position state information of the th agent in the estimated surface multi-agent system, represents the velocity state information of the th agent in the estimated surface multi-agent system, represents the weight matrix of the th agent in the estimated surface multi-agent system, and represent constants.

[0098] Define the observation error as:

[0099]

[0100] The dynamics of the observation error is:

[0101]

[0102]

[0103] Calculate the adaptive fuzzy update rate of the surface multi-agent system as:

[0104]

[0105] In the formula, and represent the design parameters of the th agent in the surface multi-agent system, which are positive constants.

[0106] S104. Based on the target mathematical model and the fuzzy state observer, determine the generalized state error introduced with a time-varying formation function;

[0107] It should be noted that in order to cope with more complex task requirements, a time-varying formation function for adjusting the formation of the surface multi-agent system is introduced into the generalized state error of the surface multi-agent system. Specifically, first determine the state error of the th agent and the th agent in the surface multi-agent system with respect to position as:

[0108]

[0109]

[0110] In the formula, when represents the leader, is changed to , in the multi-agent system on the water surface, there is a leader, and the position and state information of the leader is known. The mathematical model of the leader is:

[0111]

[0112]

[0113] In the formula, represents the position and state of the leader, represents the velocity state of the leader, represents an unknown bounded function.

[0114] When determining the generalized state error of the th agent in the multi-agent system on the water surface, it is:

[0115]

[0116]

[0117]

[0118]

[0119] In the formula, represents the time-varying formation function used to adjust the formation of the multi-agent system on the water surface, represents the communication quality between the th agent and the th agent in the multi-agent system on the water surface, represents the weighting of the communication quality between the th agent and all other agents in the multi-agent system on the water surface, is an adjacency matrix. When represents the leader, in the formula is changed to .

[0120] S105. According to the sliding mode control algorithm, the target control input of the multi-agent system on the water surface is calculated based on the generalized state error.

[0121] It should be noted that considering the convergence problem of the generalized state error, a time-varying sliding mode control method is adopted. In this way, while adjusting the formation by changing the time-varying function, the finite-time theory is applied to enable the multi-agent system on the water surface to achieve formation in a finite time.

[0122] Compared with the prior art, the present application uses a fuzzy state observer to accurately estimate the unmeasurable information in the surface multi-agent system, solves the output feedback problem of the multi-agent system, effectively reduces the dependence of the controller on the speed state information of a single ship, and while solving problems such as model uncertainty, unknown speed state information, input saturation, and uncertain external interference in the multi-agent system, effectively improves the control accuracy.

[0123] Furthermore, the present application combines a time-varying formation function with a sliding mode control method, and proposes a new type of time-varying sliding mode control method, enabling the formation of the surface multi-agent system to change with time. Compared with the traditional time-invariant formation, the flexibility of this time-varying formation is improved.

[0124] In order to better calculate the target control input, in some embodiments, as Figure 2 shown, step S105 specifically includes:

[0125] S201. Determine the time-varying sliding mode variable based on the generalized state error;

[0126] S202. Determine the time-varying sliding mode surface based on the time-varying sliding mode variable;

[0127] S203. Calculate the target control input based on the time-varying sliding mode surface.

[0128] Furthermore, considering the singularity problem of the sliding mode control, in some embodiments, the system state space is divided into two regions, and a time-varying terminal sliding mode surface and a time-varying linear auxiliary sliding mode surface are respectively designed, as well as the corresponding time-varying terminal sliding mode controller and time-varying linear auxiliary sliding mode controller. When encountering the singularity problem, switch from the time-varying terminal sliding mode to the time-varying linear auxiliary sliding mode to improve the control accuracy of the surface multi-agent system. Specifically, the time-varying terminal sliding mode variable and the time-varying linear auxiliary sliding mode variable are respectively:

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] In the formula, represents the time-varying terminal sliding mode variable of the th agent in the surface multi-agent system, represents the generalized state error of the th agent in the surface multi-agent system, denotes a positive constant, denotes a constant, denotes a matrix with diagonal elements 、 and . denotes a matrix with diagonal elements 、 and . denotes the sign function, 、 and denote the first, second, and third components of the generalized state error of the -th agent in the surface multi-agent system, and denotes the time-varying linear auxiliary sliding mode variable of the -th agent in the surface multi-agent system.

[0135] The corresponding time-varying terminal sliding mode surface and time-varying linear auxiliary sliding mode surface are respectively:

[0136]

[0137]

[0138] In the formula, denotes the time-varying terminal sliding mode surface of the -th agent in the surface multi-agent system, and denotes the time-varying linear auxiliary sliding mode surface of the

[0139] Figure 3 Considering the actuator saturation problem, in some embodiments, as shown in

[0140] S301. Calculate the initial control input based on the time-varying sliding mode surface;

[0141] In a specific embodiment, the initial control input is:

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] ​

[0148]

[0149]

[0150] In the formula, represents the initial control input, represents the initial control input corresponding to the time-varying terminal sliding mode surface, represents the initial control input corresponding to the time-varying linear auxiliary sliding mode surface, represents the th observation error of the position state information of the th agent in the multi-agent system on the water surface, represents the

[0151] S302. Based on the initial control input, calculate the target control input considering actuator saturation.

[0152] In a specific embodiment, the target control input is:

[0153]

[0154] In the formula, represents the target control input considering actuator saturation, represents the initial control input, represents the sign function, represents the saturation boundary.

[0155] Considering that the traditional fixed-time sampling mechanism will waste a large amount of network resources and communication bandwidth, in some embodiments, a dynamic event-triggering mechanism is designed at the controller end of the water surface agent. Without affecting the formation behavior and control objectives, the update frequency of the control input is reduced to save the communication resources required for the transmission of control signals. Specifically, the method further includes: determining the actual control input based on the target control input, and the actual control input is:

[0156]

[0157]

[0158]

[0159] In the formula, represents the actual control input at time represents the target control input at time represents the triggering time, Represents the measurement error of the control input, Represents The target control input at time And Represents a positive integer.

[0160] Thus, the controller has been calculating the target control input at each moment. Only at the triggering moment, the controller transmits the target control input to the actuator, and the actuator updates the actual control input. Whether the actual control input is updated depends on the measurement error of the control input. Before the next event triggering moment, the actual control input remains the target control input at the previous triggering moment. .

[0161] To better implement a control method for a surface multi-agent system in an embodiment of the present application, based on a control method for a surface multi-agent system, correspondingly, as Figure 4 shown, the embodiment of the present application further provides an output feedback control device 400 for a surface multi-agent system, including:

[0162] A model construction unit 401, configured to use the position and speed information of the agent as state variables to construct an initial mathematical model of the surface multi-agent system;

[0163] A fuzzy observation unit 402, configured to approximate the non-linear function in the initial mathematical model according to the universal approximation principle of the fuzzy logic system to obtain a target mathematical model, and construct a fuzzy state observer for estimating the unmeasurable state in the target mathematical model according to the input and output of the target mathematical model;

[0164] A sliding mode control unit 403, configured to determine a generalized state error introducing a time-varying formation function based on the target mathematical model and the fuzzy state observer, and calculate the target control input of the surface multi-agent system based on the generalized state error according to the sliding mode control algorithm.

[0165] The output feedback control device 400 for a surface multi-agent system provided in the above embodiment can implement the technical solutions described in the embodiment of the control method for a surface multi-agent system. The specific implementation principles of the above units can be referred to the corresponding content in the embodiment of the control method for a surface multi-agent system, and will not be elaborated here.

[0166] The above has introduced in detail a control method for a multi-agent system facing the water surface. In this article, specific examples are used to elaborate on the principle and implementation manner of this application. The description of the above embodiments is only used to help understand the method and its core idea of this application; at the same time, for those skilled in the art, according to the idea of this application, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to this application.

[0167] As described above, the above is only a preferred specific implementation manner of this application, but the protection scope of this application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by this application should be covered within the protection scope of this application.

Claims

1. A control method for a surface multi-agent system, characterized in that: include: The position and velocity information of the agent are used as state variables to construct the initial mathematical model of the surface multi-agent system; According to the universal approximation principle of the fuzzy logic system, the nonlinear function in the initial mathematical model is approximated to obtain the target mathematical model; According to the input and output of the target mathematical model, a fuzzy state observer is constructed for estimating the unmeasurable state in the target mathematical model; Based on the target mathematical model and the fuzzy state observer, determining a generalized state error that introduces a time-varying formation function; According to the sliding mode control algorithm, the target control input of the surface multi-agent system is obtained based on the generalized state error calculation; The generalized state error is: In the formula, Represents the first The generalized state error of an agent, Represents the estimated The position status information of each agent, It is used to adjust the first The time-varying formation function of the formation of the agents, It is used to adjust the first The formation of the agents is a time-varying formation function, Represents the first The agent and The quality of communication between agents, Represents the first The weighted value of the communication quality between an agent and all other agents, is an adjacency matrix, when When the leader is represented, Change to , Represents the first The position status information of each agent.

2. The control method for a surface multi-agent system according to claim 1, characterized in that: The initial mathematical model is: In the formula, Represents the first The position status information of each agent, Represents the first The speed state information of each agent, Represents the first The external disturbance to which an agent is subjected, Represents the first The target control input of an agent is represents a nonlinear function; The target mathematical model is: In the formula, Represents the first The optimal weight matrix for each agent is Represents the first The fuzzy basis function of each agent is Represents the estimated The speed state information of each agent, Represents the first The fuzzy minimum approximation error of the agents, Represents the first The approximation error of an agent.

3. The control method for a surface multi-agent system according to claim 2, characterized in that: The fuzzy state observer is: In the formula, Represents the estimated The position status information of each agent, Represents the estimated The speed state information of each agent, Represents the estimated The weight matrix of each agent, and Represents a constant.

4. The control method for a surface multi-agent system according to claim 1, characterized in that: According to the sliding mode control algorithm, the target control input of the surface multi-agent system is obtained based on the generalized state error calculation, including: Based on the generalized state error, determining a time-varying sliding mode variable; Determining a time-varying sliding mode surface based on the time-varying sliding mode variable; Based on the time-varying sliding surface, a target control input is calculated.

5. The control method for a surface multi-agent system according to claim 4, characterized in that: The time-varying sliding mode variables include time-varying terminal sliding mode variables and time-varying linear auxiliary sliding mode variables, the time-varying sliding mode surface includes a time-varying terminal sliding mode surface and a time-varying linear auxiliary sliding mode surface, and the time-varying linear auxiliary sliding mode surface is used to switch from the time-varying terminal sliding mode surface to the time-varying linear auxiliary sliding mode surface when encountering a singularity problem.

6. The control method for a surface multi-agent system according to claim 5, characterized in that: The time-varying terminal sliding mode variable and the time-varying linear auxiliary sliding mode variable are respectively: In the formula, Represents the first The time-varying terminal sliding mode variables of the agents, Represents the first The time-varying linear auxiliary sliding mode variables of the agents, Represents the first The generalized state error of an agent, represents a normal number, represents a constant, The diagonal elements are , and The matrix of The diagonal elements are , and The matrix of represents the symbolic function, , and Represents the first Agent generalized state error The 1st, 2nd and 3rd components of .

7. The control method for a surface multi-agent system according to claim 6, characterized in that: Based on the time-varying sliding surface, the target control input is calculated, including: Based on the time-varying sliding surface, an initial control input is calculated; Based on the initial control input, a target control input after considering actuator saturation is calculated.

8. The control method for a surface multi-agent system according to claim 7, characterized in that: The method further includes: determining an actual control input based on the target control input, wherein the actual control input is: In the formula, express The actual control input at the moment, express The target control input at the moment, represents the measurement error of the control input, express The target control input at the moment, and Represents a positive integer.

9. An output feedback control device for a surface multi-agent system, characterized in that: include: A model building unit, used to build an initial mathematical model of the surface multi-agent system by taking the position and velocity information of the agent as state variables; A fuzzy observation unit, used to approximate the nonlinear function in the initial mathematical model according to the universal approximation principle of the fuzzy logic system to obtain a target mathematical model, and to construct a fuzzy state observer for estimating the unmeasurable state in the target mathematical model according to the input and output of the target mathematical model; A sliding mode control unit, used for determining a generalized state error introducing a time-varying formation function based on the target mathematical model and the fuzzy state observer, and obtaining a target control input of the surface multi-agent system based on the generalized state error calculation according to a sliding mode control algorithm; The generalized state error is: In the formula, Represents the first The generalized state error of an agent, Represents the estimated The position status information of each agent, It is used to adjust the first The time-varying formation function of the formation of the agents, It is used to adjust the first The time-varying formation function of the formation of the agents, Represents the first The agent and The quality of communication between agents, Represents the first The weighted value of the communication quality between an agent and all other agents, is an adjacency matrix, when When the leader is represented, Change to , Represents the first The position status information of each agent.

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