Hysteresis-consistent PD control method for multi-agent systems under topological attack

Abstract

The present invention provides a hysteresis consistency PD control method for a multi-agent system subjected to topological attacks, the method comprising: establishing a mathematical model and a virtual leader model of the multi-agent system; introducing a successful and recoverable topological attack; defining an error model of the multi-agent system; designing a suitable PD control protocol; constructing a corresponding Lyapunov functional for obtaining a condition under which the multi-agent system can achieve hysteresis consistency; and achieving hysteresis consistency of the multi-agent system subjected to topological attacks based on PD control. The present invention reduces the required computing resources, makes it easy to obtain the control amount, and has a wider range of applications.

Description

Technical Field

[0001] The present invention relates to the field of collaborative control technology, and in particular to a delayed consistency PD control method for a multi-agent system subjected to topological attacks. Background Art

[0002] In recent years, the cooperative control of multi-agent systems has played an important role in the fields of military, smart factories, and medical care. In particular, as an important research direction in the cooperative control of multi-agent systems, consistency has received extensive attention and obtained a large number of meaningful results. Furthermore, considering that the acquisition of the position and speed information of the virtual leader must be ahead of the acquisition of the position and speed information of the agent itself, some researchers have further studied the delayed consistency control problem of multi-agent systems and established some important results.

[0003] Furthermore, in many cases, the communication topology of a multi-agent system may be destroyed due to various forms of attacks, resulting in the multi-agent system failing to achieve the desired dynamic behavior. Therefore, it is very necessary to consider the impact of topological attacks when studying the hysteresis consistency of a multi-agent system. However, there is still a lack of research on the hysteresis consistency control of a multi-agent system that suffers from topological attacks.

[0004] On the other hand, considering that derivative control can not only improve the response speed of the system but also improve the stability of the system, it is obviously very meaningful and challenging to use the PD control method to study the hysteresis consistency problem of multi-agent systems suffering from topological attacks. Summary of the invention

[0005] The purpose of the present invention is to provide a delayed consistency (PD) control method for a multi-agent system subjected to a topology attack, so as to solve the delayed consistency control problem of the multi-agent system subjected to a topology attack.

[0006] The present invention is implemented by a delayed consistency PD control method for a multi-agent system subjected to a topological attack, the method comprising:

[0007] Establish mathematical models of multi-agent systems and virtual leader models;

[0008] Introducing successful and recoverable topological attacks;

[0009] Define the error model for multi-agent systems;

[0010] Design a suitable PD control protocol;

[0011] Construct the corresponding Lyapunov functional to obtain the conditions for the multi-agent system to achieve delayed consistency;

[0012] Achieving delayed consistency in a multi-agent system subjected to topological attacks based on PD control.

[0013] As a further solution of the present invention: the mathematical model of the multi-agent system is:

[0014] ;

[0015] in, , , and Respectively represent intelligent agents The position vector, velocity vector and control input, represent dimension column vector, is the time variable, Represents the nonlinear dynamics of the agent.

[0016] As a further solution of the present invention: the virtual leader model of the multi-agent system is:

[0017] ;

[0018] in, , Represent the position vector and velocity vector of the virtual leader respectively.

[0019] As a further solution of the present invention: the multi-agent system suffers a successful and recoverable attack, and the communication topology is ( is a positive integer) is destroyed due to the attack, When recovery, , , represents a positive integer, when hour, , is a The known real number matrix of dimension represents the interaction intensity between agents, where is defined as follows:

[0020] ;

[0021] is a dimensional known matrix, representing the The interaction strength between agents under topological attacks, where and have the same definition, , Represents the number of classes of topological attacks suffered by the multi-agent system. For convenience, it is defined as follows:

[0022] ;

[0023] in , is a -dimensional real matrix.

[0024] As a further solution of the present invention: design the following PD control protocol:

[0025] ;

[0026] in , is a normal number, Is symmetrical -dimensional real matrix and positive definite.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] The present invention proposes a hysteresis-consistent PD control method for a multi-agent system subjected to topology attacks; a solution is provided for the situation where the communication topology of the multi-agent system is destroyed due to topology attacks; from an implementation perspective, the present invention requires fewer computing resources and the required control quantities are easier to obtain; the hysteresis-consistent PD control method for a multi-agent system subjected to topology attacks 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

[0029] Figure 1 Flow chart of the hysteresis-consistent PD control method for a multi-agent system subjected to topological attack;

[0030] Figure 2 It is a first simulation result analysis diagram of the present invention;

[0031] Figure 3 This is a second simulation result analysis diagram of the present invention. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with 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 used to limit the present invention.

[0033] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0034] like Figure 1 As shown, an embodiment of the present invention provides a hysteresis consistency PD control method for a multi-agent system subjected to a topology attack, the method comprising:

[0035] Establish mathematical models of multi-agent systems and virtual leader models;

[0036] Introducing successful and recoverable topological attacks;

[0037] Define the error model for multi-agent systems;

[0038] Design a suitable PD control protocol;

[0039] Construct the corresponding Lyapunov functional to obtain the conditions for the multi-agent system to achieve delayed consistency;

[0040] Achieving delayed consistency in a multi-agent system subjected to topological attacks based on PD control.

[0041] In the embodiments of the present invention, a solution is provided for the situation where the communication topology of a multi-agent system is destroyed due to a topology attack; from an implementation perspective, the present invention requires fewer computing resources and the required control quantity is easier to obtain; the delayed consistency PD control method for a multi-agent system subjected to a topology attack 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.

[0042] As a preferred embodiment of the present invention, the mathematical model of a single agent in a multi-agent system is constructed as follows:

[0043] Formula (1) ;

[0044] in , , and Respectively represent intelligent agents The position vector, velocity vector and control input, represent dimension column vector, is the time variable, represents the nonlinear dynamics of the agent and satisfies the following inequality:

[0045] Formula (2) ;

[0046] For any ,in is a normal number.

[0047] In order to obtain the desired results, the virtual leaders are selected as follows:

[0048] Formula (3) ;

[0049] in, , Represent the position vector and velocity vector of the virtual leader respectively.

[0050] As a preferred embodiment of the present invention, the multi-agent system can achieve hysteresis consistency if for any The following conditions must be met:

[0051] ;

[0052] in is a positive constant representing the time lag between the agent and the virtual leader.

[0053] As a preferred embodiment of the present invention, we define and , the error model can be obtained from formulas (1) and (3) as follows:

[0054] Formula (4) ;

[0055] in .

[0056] As a preferred embodiment of the present invention, the multi-agent system suffers a successful and recoverable attack, and the communication topology is ( is a positive integer) is destroyed due to the attack, When recovery, , , represents a positive integer, when hour, . is a The known real number matrix of dimension represents the interaction intensity between agents, where is defined as follows:

[0057] ;

[0058] is a dimensional known matrix, representing the The interaction strength between agents under topological attacks, where and have the same definition, , Represents the number of classes of topological attacks suffered by the multi-agent system. For convenience, it is defined as follows:

[0059] ;

[0060] in , is a -dimensional real matrix.

[0061] As a preferred embodiment of the present invention, considering that differential control can enhance the stability of the closed-loop system and improve the response speed of the system, the following PD control protocol is proposed:

[0062] Formula (5) ;

[0063] in , is a normal number, Is symmetrical -dimensional real matrix and positive definite.

[0064] According to formulas (4) and (5), we can get

[0065] Formula (6)

[0066] in .

[0067] As a preferred embodiment of the present invention, if there is , , So that the following inequality holds:

[0068] Formula (7) ;

[0069] in, , , then the multi-agent system supported by formula (1) can achieve hysteresis consistency under the action of the PD control protocol supported by formula (5).

[0070] For convenience, the definition is as follows:

[0071] ;

[0072] ;

[0073] ;

[0074] ;

[0075] .

[0076] The following Lyapunov functional is constructed for the system supported by formula (6):

[0077] Formula (8) ;

[0078] in , , .

[0079] Taking the derivative of the above formula, we can get

[0080] Formula (9) ;

[0081] In addition, formula (8) can be used to obtain

[0082] Formula (10) ;

[0083] Based on nonlinear function The assumption is that

[0084] Formula (11) ;

[0085] Combining formulas (9)-(11), we can get

[0086] Formula (12) ;

[0087] in , , represent The maximum eigenvalue of represent The maximum eigenvalue of .

[0088] From formula (12), we can deduce

[0089] Formula (13) ;

[0090] According to formula (13), we can get

[0091] Formula (14) ;

[0092] From formulas (10) and (14), we can get

[0093] Formula (15) ;

[0094] Based on formula (15), we can get

[0095] ;

[0096] in .

[0097] Therefore, the multi-agent system supported by formula (1) can achieve hysteresis consistency under the action of the PD control protocol supported by formula (5).

[0098] As an extended embodiment of the present invention, an example is selected for simulation verification;

[0099] Consider the following nonlinear second-order multi-agent system:

[0100] Formula (16) ;

[0101] in , and Respectively represent intelligent agents The control input, position vector and velocity vector; , .

[0102] Obviously, The following inequality is satisfied:

[0103] ;

[0104] For any .Pick ,

[0105] ;

[0106] ;

[0107] ;

[0108] With the help of the YALMIP toolbox in MATLAB, the following parameters can be obtained to make condition (7) true:

[0109] ;

[0110] According to formula (7), the multi-agent system supported by formula (16) can achieve hysteresis consistency under the action of the PD control protocol supported by formula (5). , , . , The change process of Figure 2 and Figure 3 As shown. Figure 2 and Figure 3 It can be seen that the multi-agent system can achieve delayed consistency.

[0111] The above only describes in detail 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 protection scope of the present invention.

[0112] It should be understood that, although each step in the flow chart of each embodiment of the present invention is shown in sequence according to the indication of the arrow, these steps are not necessarily performed in sequence according to the order indicated by the arrow. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, 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.

[0113] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application 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. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0114] 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, which follow the general principles of the present disclosure and include common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the claims.

Claims

1. A hysteresis-consistent PD control method for a multi-agent system subjected to topological attack, characterized in that: The method comprises: Establish mathematical models of multi-agent systems and virtual leader models; Introducing a successful and recoverable topology attack: The multi-agent system is attacked successfully and recoverably, and the communication topology is 2v+1 , when v is a positive integer, it is destroyed due to the attack. 2(v+1) When recovery, represents a positive integer. When v→+∞, t 2v+1 →+∞,F=(F αr ) h×h is an h×h dimensional known real number matrix representing the interaction strength between agents, where F αr is defined as follows: is an h×h dimensional known matrix, representing the interaction intensity between agents under the mth topological attack, where With F αr The same definition is used, m = 1, 2, ..., μ, where μ represents the number of topological attacks suffered by the multi-agent system; for convenience, it is defined as follows: in is an h×h dimensional real matrix; Define the error model for multi-agent systems; Design PD control protocol: Among them, ξ1,ξ2 are positive constants, ω1,ω2,B is a symmetric a×a dimensional real matrix and positive definite, k is a positive constant, representing the time lag between the agent and the virtual leader. and β α (t) represent the position vector and velocity vector of agent α, respectively. and β0(t) represent the position vector and velocity vector of the virtual leader, respectively; A multi-agent system can achieve delayed consistency if the following conditions are satisfied for any α=1,2,Λ,h: Where k is a positive constant, representing the time lag between the agent and the virtual leader; The corresponding Lyapunov functional S(t) is constructed to obtain the conditions for the multi-agent system to achieve delayed consistency: Formula(8) in Taking the derivative of the above formula, we get: Formula(9) In addition, through formula (8) we get: Formula (10)ρ min (Q2)‖φ(t)‖ 2 ≤S(t)≤ρ max (Q2)‖φ(t)‖ 2 ; Among them, ρ max (Q2) represents the maximum eigenvalue of Q2, ρ min (Q2) represents the minimum eigenvalue of Q2, Based on nonlinear function The assumption is: Formula (11) Combining formulas (9)-(11), we get: Formula(12) in ρ max (Q1) represents the maximum eigenvalue of Q1, ρ max (Q2) represents the maximum eigenvalue of Q2, From formula (12), we can deduce: Official(13) According to formula (13), we get: Official(14) From formulas (10) and (14), we can obtain: Official(15) Based on formula (15), we get: Achieving delayed consistency in a multi-agent system subjected to topological attacks based on PD control.

2. The hysteresis consistency PD control method for a multi-agent system subjected to topology attack according to claim 1 is characterized in that: The mathematical model of the multi-agent system is: Where, α=1,2,...,h, and Represent the position vector, velocity vector and control input of agent α respectively, represents an a-dimensional column vector, t is the time variable, Represents the nonlinear dynamics of the agent.

3. The hysteresis consistency PD control method for a multi-agent system subjected to topology attack according to claim 1 is characterized in that: The virtual leader model of the multi-agent system is: in, represent the position vector and velocity vector of the virtual leader respectively.

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