Delayed H-infinite consistency PI control method for multi-robot systems under attack

Abstract

The present invention provides a PI control method for delayed H-infinity consistency of a multi-robot system under attack, the method comprising: constructing a mathematical model and a virtual leader model of the multi-robot system; introducing a successful and recoverable topological attack; defining an error model of the multi-robot system; designing a PI control strategy; constructing a corresponding Lyapunov functional to obtain a criterion for delayed H-infinity consistency of the multi-robot system; and realizing delayed H-infinity consistency of the multi-robot system under attack based on PI control.

Description

Technical Field

[0001] The invention relates to the technical field of cooperative control, and in particular to a hysteresis H infinite consistency PI control method for a multi-robot system under attack. Background Art

[0002] As an important research direction in the coordinated control of multi-robot systems, consensus has received extensive attention and obtained a large number of important results. However, given that the acquisition of the virtual leader's position and velocity information is often earlier than the acquisition of the robot's own information and that robots are often affected by external interference (such as environmental noise, wind force, friction vibration, etc.) in actual operation, some researchers have conducted research on the delayed H-infinity consensus control problem of multi-robot systems and achieved some meaningful results.

[0003] Furthermore, the communication topology has an important influence on the lagged H-infinity consistency of the multi-robot system. However, the communication topology of the multi-robot system may be destroyed due to attacks, which makes the multi-robot system unable to achieve lagged H-infinity consistency. Therefore, it is very meaningful to consider the impact of topological attacks when studying the lagged H-infinity consistency of the multi-robot system. However, there is still a lack of research on the lagged H-infinity consistency control of the multi-robot system under topological attacks.

[0004] In addition, considering that integral control can not only eliminate static errors but also make the closed-loop system have better stability, it is obviously very meaningful to use PI control method to study the delayed H-infinity consistency of multi-robot systems subjected to topological attacks. Summary of the invention

[0005] The purpose of the present invention is to provide a delayed H-infinity consistency PI control method for a multi-robot system under attack, so as to solve the delayed H-infinity consistency control problem of the multi-robot system under the influence of topological attack.

[0006] The present invention is implemented by a hysteresis H infinite consistency PI control method for a multi-robot system under attack, the method comprising:

[0007] Construct mathematical models and virtual leader models of multi-robot systems;

[0008] Introducing successful and recoverable topological attacks;

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

[0010] Design PI control protocol;

[0011] The corresponding Lyapunov functional is constructed to obtain the criterion for the delayed H-infinity consistency of the multi-robot system;

[0012] A multi-robot system subjected to topological attack achieves delayed H-infinity consistency based on PI control.

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

[0014] ;

[0015] in, , represents the nonlinear dynamics of the robot, , and Respectively represent robots The position vector, velocity vector and control input, is the time variable, Representative robot external interference and any satisfy:

[0016] .

[0017] As a further solution of the present invention: the virtual leader model of the multi-robot system is

[0018] ;

[0019] in, , represent the position vector and velocity vector of the virtual leader respectively.

[0020] As a further aspect of the present invention: and ; According to the mathematical model of the multi-robot system and the virtual leader model, the following error model is obtained:

[0021] ;

[0022] in .

[0023] As a further solution of the present invention: When the multi-robot system is attacked, the communication topology is destroyed. When recovery, , , represents a positive integer, when hour, . is a dimensional real matrix, representing the interaction strength between agents, where is defined as follows:

[0024] ;

[0025] is a dimensional real 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-robot system. For convenience, define:

[0026] ;

[0027] in , is a Dimensional real matrix.

[0028] As a further solution of the present invention: design the following PI control protocol:

[0029] ;

[0030] in , is a normal number, yes dimensional real matrix and positive definite.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The present invention proposes a hysteresis H-infinity consistent PI control method for a multi-robot system under attack; a solution is provided for the situation where the communication topology of the multi-robot 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 hysteresis H-infinity consistent PI control method for a multi-robot system under attack is applicable to any actual system modeled by the mathematical model of the multi-robot system considered by the present invention, and has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Flow chart of the hysteresis H infinite consistency PI control method for the multi-robot system under attack;

[0034] Figure 2 This is a first simulation result analysis diagram of the present invention.

[0035] Figure 3 This is a second simulation result analysis diagram of the present invention. DETAILED DESCRIPTION

[0036] 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.

[0037] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0038] like Figure 1 As shown, an embodiment of the present invention provides a hysteresis H infinite consistency PI control method for a multi-robot system under attack, the method comprising:

[0039] Construct mathematical models and virtual leader models of multi-robot systems;

[0040] Introducing successful and recoverable topological attacks;

[0041] Define the error model for multi-robot systems;

[0042] Design PI control protocol;

[0043] The corresponding Lyapunov functional is constructed to obtain the criterion for the delayed H-infinity consistency of the multi-robot system;

[0044] A multi-robot system subjected to topological attack achieves delayed H-infinity consistency based on PI control.

[0045] In an embodiment of the present invention, a solution is provided for the situation where the communication topology of a multi-robot 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 hysteresis H infinite consistency PI control method for the attacked multi-robot system is applicable to any actual system modeled by the mathematical model of the multi-robot system considered by the present invention, and has a wide range of applications.

[0046] As a preferred embodiment of the present invention, the mathematical model of a single robot in a multi-robot system is constructed as follows:

[0047] Formula (1) ;

[0048] in, , represents the nonlinear dynamics of the robot, , , Respectively represent robots The position vector, velocity vector and control input, is the time variable, Representative robot external interference and any satisfy:

[0049] ;

[0050] Assumptions The following inequality is satisfied:

[0051] Formula (2) ;

[0052] For any ,in is a normal number.

[0053] In order to obtain the desired results, the virtual leaders are selected as follows:

[0054] Formula (3) ;

[0055] in, , represent the position vector and velocity vector of the virtual leader respectively.

[0056] As a preferred embodiment of the present invention, the multi-robot system can achieve delayed H-infinity consistency if the following conditions are met:

[0057] ;

[0058] For any ,in , , , , represents the time lag between the agent and the virtual leader;

[0059] As a preferred embodiment of the present invention, it is defined as and According to formulas (1) and (3), the following error model can be obtained:

[0060] Formula (4) ;

[0061] in .

[0062] As a preferred embodiment of the present invention, When the multi-robot system is attacked, the communication topology is destroyed. When recovery, , , represents a positive integer, when hour, . is a dimensional real matrix, representing the interaction strength between agents, where is defined as follows:

[0063] ;

[0064] is a dimensional real 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-robot system. For convenience, define

[0065] ;

[0066] in , is a Dimensional real matrix.

[0067] As a preferred embodiment of the present invention, considering that integral control can eliminate static errors, the following PI control protocol is proposed:

[0068] Formula (5) ;

[0069] in , is a normal number, yes dimensional real matrix and positive definite.

[0070] According to formulas (4) and (5), we can get

[0071] Formula (6) ;

[0072] in , , .

[0073] As a preferred embodiment of the present invention, if there is , , , So that the following inequality holds:

[0074] Formula (7) ;

[0075] in, , , then the multi-robot system supported by formula (1) can achieve hysteresis H infinite consistency under the action of the PI controller supported by formula (5).

[0076] For convenience, define:

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] ;

[0084] The following Lyapunov functional is constructed for the multi-robot system supported by formula (6):

[0085] Formula (8) ;

[0086] According to formula (3), we can get

[0087] Formula (9)

[0088] Using formulas (8) and (9), we can get

[0089] Formula (10) ;

[0090] in .

[0091] From formula (10), we can get

[0092] ;

[0093] Therefore, the multi-robot system supported by formula (1) can achieve delayed H-infinity consistency under the action of the PI control protocol supported by formula (5).

[0094] As an extended embodiment of the present invention, an example is selected for simulation verification;

[0095] Consider the following nonlinear second-order multi-robot system:

[0096] Formula (11) ;

[0097] in, , , and Respectively represent intelligent agents Control input, external disturbance, position vector and velocity vector; ;

[0098] .

[0099] Obviously, The following inequality is satisfied:

[0100] ;

[0101] For any .Pick ,

[0102] ;

[0103] ;

[0104] ;

[0105] With the help of the YALMIP toolbox in MATLAB, we can get Satisfies formula (7).

[0106] According to formula (7), the multi-robot system supported by formula (11) can achieve hysteresis H infinite consistency under the action of the PI controller supported by formula (5). Let . The change process of Figure 2 and Figure 3 As shown. Figure 2 and Figure 3 It can be seen that the multi-robot system can achieve delayed H-infinity consistency.

[0107] 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.

[0108] 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.

[0109] 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).

[0110] 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 H infinite consistency PI control method for a multi-robot system under attack, characterized in that: The method comprises: Construct mathematical models and virtual leader models of multi-robot systems; Introducing a successful and recoverable topological attack: At t = t 2d+1 When t=t 2(d+1) When it recovers, 0=t0<t1<t2<…<t 2d+1 <t 2(d+1) <…, represents a positive integer. When d→+∞, t 2d+1 →+∞;Q=(Q ηr ) j×j is a j×j dimensional real matrix representing the interaction intensity between agents, where is defined as follows: is a j×j dimensional real matrix, representing the interaction intensity between agents under the nth topological attack, where With Q ηr The same definition is used, n = 1, 2, ..., o, where o represents the number of topological attacks suffered by the multi-robot system; for convenience, we define: in is a j×j dimensional real matrix; Define the error model for multi-robot systems; A multi-robot system can achieve delayed H-infinity consistency if the following conditions hold: For any where ξ η (t) = (α η (t)-α0(tz)) T (α η (t)-α0(tz))+(γ η (t)-γ0(tz)) T (γ η (t)-γ0(tz)), represents the time lag between the agent and the virtual leader, and denote the position vector and velocity vector of robot η respectively, represent the position vector and velocity vector of the virtual leader respectively, represents the external disturbance of robot η; Design PI control protocol: Where ρ1, ρ2 are positive constants, υ1, υ2, C are k×k dimensional real matrices and are positive definite; The corresponding Lyapunov functional V1(t) is constructed to obtain the criterion for the delayed H-infinity consistency of the multi-robot system: Formula(8) Formula(9) Using formulas (8) and (9), we get: Formula (10) in From formula (10), we get: A multi-robot system subjected to topological attack achieves delayed H-infinity consistency based on PI control.

2. The method for controlling a multi-robot system under attack with delayed H infinity consistency PI according to claim 1, characterized in that: The mathematical model of the multi-robot system is: Where η=1,2,...,j, represents the nonlinear dynamics of the robot, and They represent the position vector, velocity vector and control input of robot η respectively, t is the time variable, represents the external disturbance of the robot η and for any satisfy:

3. The method for controlling a multi-robot system under attack with delayed H infinity consistency PI according to claim 1, characterized in that: The virtual leader model of the multi-robot system is: in, represent the position vector and velocity vector of the virtual leader respectively.

4. The method for controlling a multi-robot system under attack with delayed H infinity consistency PI according to claim 1, characterized in that: definition and According to the mathematical model of the multi-robot system and the virtual leader model, the following error model is obtained: Where η=1,2,...,j.

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