Hysteresis Formation Control Method for Nonlinear Second-Order Multi-Agent Systems

Abstract

The present invention is applicable to the field of collaborative control, and provides a hysteresis formation control method for a nonlinear second-order multi-agent system, the method comprising: constructing a mathematical model of the multi-agent system and a virtual leader; introducing an error model, the error model comprising a position error and a speed error; designing a hysteresis formation control strategy; constructing a Lyapunov functional for obtaining the conditions under which the multi-agent system can achieve hysteresis formation. From an implementation perspective, the present invention requires fewer computing resources and the required control amount is easier to obtain, and is applicable to any actual system modeled by the mathematical model of a single agent considered by the present invention, and has a wide range of applications.

Description

Technical Field

[0001] The present invention belongs to the field of collaborative control, and in particular relates to a hysteresis formation control method for a nonlinear second-order multi-agent system. Background Art

[0002] A multi-agent system is a complex network composed of several independent agents. Its goal is to solve complex tasks through collaboration between these agents. Compared to a single agent, a multi-agent system can not only complete some tasks that a single agent cannot, but also reduce costs, increase flexibility, and improve reliability. Given this, the collaborative control of multi-agent systems has become a research hotspot in recent years.

[0003] Formation control is an important research area in the coordinated control of multi-agent systems. It involves designing appropriate control strategies for the agents so that they maintain a predetermined geometric shape and converge to the same velocity as time approaches infinity. To date, numerous research results on formation control in multi-agent systems have been reported. However, each agent's access to its own state information lags significantly behind that of the virtual leader. Therefore, further research on the problem of delayed formation control in multi-agent systems is highly valuable.

[0004] According to the existing research results on the coordinated control of multi-agent systems, the delayed formation control of multi-agent systems has not been considered. Obviously, studying the delayed formation control problem of multi-agent systems has important theoretical significance and practical application value. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a hysteresis formation control method for a nonlinear second-order multi-agent system to solve the problems existing in the above-mentioned background technology.

[0006] The present invention is implemented as follows: a hysteresis formation control method for a nonlinear second-order multi-agent system, the method comprising the following steps:

[0007] Construct mathematical models of multi-agent systems and virtual leaders;

[0008] Introducing an error model, wherein the error model includes position error and velocity error;

[0009] Designing a control strategy for delayed formations;

[0010] A Lyapunov functional is constructed to obtain the conditions under which a multi-agent system can achieve delayed formation.

[0011] As a further solution of the present invention: the mathematical model of the multi-agent system is expressed as follows:

[0012] ,

[0013] in ,and Respectively represent r The position vector, velocity vector and control input of each agent, is the time variable, represents the internal dynamics of the agent, express s -dimensional real vector.

[0014] As a further solution of the present invention: the virtual leader model is:

[0015] ,

[0016] in and represent the position vector and velocity vector of the virtual leader respectively.

[0017] As a further solution of the present invention: the hysteresis formation is defined as follows:

[0018] ,

[0019] in , represents the time lag between each agent and the virtual leader, It is an intelligent agent and the desired relative position between the virtual leader, Represents a real number.

[0020] As a further solution of the present invention: the designed hysteresis formation control strategy is:

[0021] ,

[0022] in , Represents controller parameters, is the coupling weight matrix between multiple agents. If the agent With the agent If there is communication between ;otherwise ;also, , express dimensional real matrix.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] The present invention proposes a hysteresis formation control method for a nonlinear second-order multi-agent system. Based on the fact that each agent's acquisition of its own state information lags significantly behind the acquisition of the virtual leader's state information, the present invention proposes a hysteresis formation control method for a multi-agent system for the first time. From an implementation perspective, the present invention requires fewer computing resources and the required control quantity is easier to obtain. The hysteresis formation control method for a nonlinear second-order multi-agent system is applicable to any actual system modeled by the mathematical model of a single agent considered by the present invention, and has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Flowchart of the hysteresis formation control method for nonlinear second-order multi-agent systems.

[0026] Figure 2 and Figure 3 This is an analysis diagram of the simulation results of the present invention. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0028] The specific implementation of the present invention is described in detail below with reference to specific embodiments.

[0029] like Figure 1 As shown, an embodiment of the present invention provides a hysteresis formation control method for a nonlinear second-order multi-agent system, the method comprising the following steps:

[0030] Constructing a mathematical model of a multi-agent system and a virtual leader, wherein the mathematical model of the virtual leader is selected from the mathematical model of the multi-agent system;

[0031] Introducing an error model, wherein the error model includes position error and velocity error;

[0032] Designing a control strategy for delayed formations;

[0033] A Lyapunov functional is constructed to obtain the conditions under which a multi-agent system can achieve delayed formation.

[0034] It should be noted that each agent's acquisition of its own state information lags significantly behind that of the virtual leader. Therefore, further research on the delayed formation control problem of multi-agent systems is very meaningful.

[0035] In an embodiment of the present invention, a hysteresis formation control method for a nonlinear second-order multi-agent system is proposed. Based on the fact that each agent's acquisition of its own state information lags significantly behind the acquisition of the virtual leader's state information, the present invention proposes a hysteresis formation control method for a multi-agent system for the first time. From an implementation perspective, the present invention requires fewer computing resources and the required control amount is easier to obtain. The hysteresis formation control method for a nonlinear second-order multi-agent system is applicable to any actual system modeled by the mathematical model of a single agent considered by the present invention, and has a wide range of applications.

[0036] As a preferred embodiment of the present invention, a mathematical model of a nonlinear second-order multi-agent system is constructed as follows:

[0037] (1)

[0038] in ,and Respectively represent r The position vector, velocity vector, and control input of each agent, is the time variable, is a nonlinear continuous function and satisfies the following inequality:

[0039] (2)

[0040] For any ,in and is a positive constant, express s -dimensional real vector.

[0041] The mathematical model of the virtual leader in the multi-agent system (1) is expressed as follows:

[0042] (3)

[0043] in and represent the position vector and velocity vector of the virtual leader respectively.

[0044] The multi-agent system (1) can achieve delayed formation if the following conditions are met:

[0045] ,

[0046] in , It is an intelligent agent and the time lag between the virtual leader, It is an intelligent agent and the desired relative position between the virtual leader, Represents a real number.

[0047] As a preferred embodiment of the present invention, the hysteresis formation control strategy is designed as follows:

[0048] (4)

[0049] in , Represents controller parameters, is the coupling weight matrix between multiple agents. If the agent With the agent If there is communication between ;otherwise ;also, , express dimensional real matrix.

[0050] As a preferred embodiment of the present invention, it is defined as and According to (1), (2) and (4), the error model can be obtained, which is as follows:

[0051] (5)

[0052] in , , .

[0053] In the embodiment of the present invention, if there is and The following conditions are met:

[0054] , (6)

[0055] in , then the multi-agent system (1) can realize the delayed formation under the control strategy (4).

[0056] For the error model (5), the following Lyapunov functional is constructed:

[0057] (7)

[0058] in .

[0059] Taking the derivative of the above formula, we can get

[0060] (8)

[0061] From (2), we can conclude that

[0062] (9)

[0063] (10)

[0064] According to (6) and (8)-(10), we can get

[0065] (11)

[0066] in , and denote the maximum eigenvalue and minimum eigenvalue of a real symmetric matrix, respectively.

[0067] From (11) we can get

[0068] (12)

[0069] According to (7), we can conclude that

[0070] (13)

[0071] Combining (12) and (13) we can get

[0072]

[0073] Therefore, the multi-agent system (1) can achieve delayed formation under the control protocol (4).

[0074] As a preferred embodiment of the present invention, an example is selected for simulation verification, and the following nonlinear second-order multi-agent system is considered:

[0075] (14)

[0076] in , ,and Represents the intelligent agent r Position vector, velocity vector, and control input; Obviously, The following inequality is satisfied:

[0077]

[0078] For any , Represents a 2-dimensional real vector.

[0079] choose , , , , ,and

[0080] .

[0081] Obviously, it is easy to get (6) is satisfied. Therefore, the multi-agent system (14) can realize delayed formation under the control protocol (4). Figure 2 and Figure 3 Describes the control protocol (4) and 5. The changing process. Figure 2 and Figure 3 It can be seen that as time goes by, the multi-agent system (14) can achieve delayed formation.

[0082] The above is only a detailed description of the preferred embodiments of the present invention, which is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

[0083] It should be understood that, although the various steps in the flow chart of each embodiment of the present invention are shown in sequence according to the indication of the arrows, these steps are not necessarily performed in sequence according to the order indicated by the arrows. Unless otherwise specified herein, the execution of these steps is not strictly limited in order, and these steps can be performed in other orders. Moreover, at least a portion of the steps in each embodiment may include a plurality of sub-steps or a plurality of stages, and these sub-steps or stages are not necessarily performed at the same time, but can be performed at different times, and the execution order of these sub-steps or stages is not necessarily performed in sequence, but can be performed in turn or alternately with at least a portion of other steps or sub-steps or stages of other steps.

[0084] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware through a computer program. The program can be stored in a non-volatile computer-readable storage medium. When executed, the program can include the processes of the above-described method embodiments. Any reference to memory, storage, database, or other media used in the various embodiments provided herein may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct RAMbus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM).

[0085] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the disclosure in the specification and examples. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered merely as exemplary, and the true scope and spirit of the present disclosure are indicated by the claims.

Claims

1. A hysteresis formation control method for a nonlinear second-order multi-agent system, characterized in that: The method comprises the following steps: Construct mathematical models of multi-agent systems and virtual leaders; The mathematical model of the multi-agent system is expressed as follows: ， in and Respectively represent r The position vector, velocity vector and control input of each agent, is the time variable, represents the internal dynamics of the agent, express s dimensional real vector; The virtual leader model is: ， in and represent the position vector and velocity vector of the virtual leader respectively; Introducing an error model, wherein the error model includes a position error and a velocity error; Design a delayed formation control strategy; The designed hysteresis formation control strategy is: in , Represents controller parameters, is the coupling weight matrix between multiple agents. If the agent With Agent If there is communication between ;otherwise ;also, , express dimensional real matrix; Construct Lyapunov functional to obtain the conditions under which multi-agent system can achieve delayed formation; Construct the following Lyapunov functional: (7) in and ; Taking the derivative of the above formula, we can get (8) According to the nonlinear function Assuming that it is available, (9) (10) According to (6) and (8)-(10), we can get (11) in , and denote the maximum eigenvalue and minimum eigenvalue of a real symmetric matrix respectively; From (11) we can get (12) According to (7), we can conclude (13) Combining (12) and (13) we can get ； Therefore, the multi-agent system can achieve hysteresis formation under the action of hysteresis formation control protocol; The lag formation is defined as follows: ， in , represents the time lag between each agent and the virtual leader, It is an intelligent agent and the desired relative position between the virtual leader, Represents a real number.

Images