H infinite delay formation control method for multi-agent systems with communication delay

Abstract

The present invention mainly aims at the field of cooperative control, and discloses a multi-agent system H infinite lag formation control method with communication time lag, which includes the following steps: first, constructing a multi-agent system model with external interference and a mathematical model of a virtual leader; second, based on the mathematical model of the multi-agent system and the virtual leader, obtaining an error system; then, designing a H infinite lag formation control strategy with communication time lag; finally, constructing a corresponding Lyapunov functional to analyze and derive the conditions under which the multi-agent system can realize the H infinite lag formation. From the perspective of implementation, the present invention requires fewer computing resources and the required control amount is easier to obtain.

Description

Technical Field

[0001] The invention belongs to the field of cooperative control, and in particular relates to a multi-agent system H infinite lag formation control method with communication time lag. Background Art

[0002] As one of the important research directions of cooperative control of multi-agent systems, the purpose of formation control is to design a suitable control strategy so that all agents maintain a predetermined geometric shape and the speed tends to be the same when time tends to infinity. So far, many research results on formation control of multi-agent systems have been reported. In fact, each agent's acquisition of its own state information lags significantly behind the acquisition of the virtual leader's state information. In view of this, further research on the lagging formation control problem of multi-agent systems has important theoretical significance.

[0003] In the process of realizing formation, communication between agents will cause time delay due to many factors (such as information congestion, limited transmission speed, etc.). So far, the formation control problem of multi-agent systems with communication time delay has been preliminarily studied. In addition, considering that multi-agent systems are often affected by some external interferences, such as wind, noise, temperature, etc. Therefore, some researchers have also preliminarily studied the H-infinite formation control problem of multi-agent systems with communication time delay and external interference.

[0004] However, according to the existing research results on the cooperative control of multi-agent systems, the H infinite lag formation control problem of multi-agent systems with communication delay and external interference has not been considered. Obviously, studying the H infinite lag formation control problem of multi-agent systems with communication delay and external interference has important theoretical significance and practical application value. Summary of the invention

[0005] The purpose of the embodiments of the present invention is to provide a method for controlling an H infinite lag formation of a multi-agent system with communication time lag, aiming to solve the H infinite lag formation control problem of a multi-agent system with communication time lag and external interference which has not been considered so far.

[0006] The embodiment of the present invention is implemented as follows: a multi-agent system H infinite delay formation control method with communication time delay, the method comprising:

[0007] Construct a mathematical model of a multi-agent system with external interference and a virtual leader;

[0008] Based on the mathematical model of multi-agent system and virtual leader, the error system is obtained;

[0009] Design a H infinite-delay formation control strategy with communication delay;

[0010] The corresponding Lyapunov functional is constructed to analyze and derive the conditions under which the multi-agent system can realize H infinite lag formation.

[0011] A control method for H infinite lag formation of a multi-agent system with communication time delay, the steps are as follows:

[0012] Step 1: Construct the mathematical model of the multi-agent system with external interference as follows:

[0013]

[0014] In the above formula, and Represent the position vector, velocity vector and control input of agent c respectively, and Respectively represent the derivatives of the position vector and velocity vector of agent c, represents the internal dynamics of the agent, t is the time variable, represents an a-dimensional real vector, Indicates external interference and satisfies

[0015]

[0016] For any represents the time variable; is a nonlinear function and satisfies the following inequality:

[0017] ||δ(t,o1,o2)-δ(t,o3,o4)||≤q1||o1-o3||+q2||o2-o4||;

[0018] For any where q1 and q2 are positive constants.

[0019] The mathematical model of the virtual leader of the multi-agent system is expressed as follows:

[0020]

[0021] In the above formula, and represent the position vector and velocity vector of the virtual leader respectively, and denote the derivatives of the position vector and velocity vector of the virtual leader, respectively. represents the internal dynamics of the virtual leader, t is the time variable, represents an a-dimensional real vector.

[0022] Step 2: The multi-agent system H infinite lag formation with communication time delay is defined as follows:

[0023]

[0024] For any s1 represents the time variable, l represents the number of agents in the multi-agent system, where m is a normal number, and Represent the position vector and velocity vector of agent c respectively, and represent the position vector and velocity vector of the virtual leader respectively, represents an a-dimensional real vector, represents the time lag between agent c and the virtual leader, and denote the position vector and velocity vector of the virtual leader with a time lag α, respectively. is the expected relative position between agent c and the virtual leader, V(·) is a non-negative function, represents a real number, Indicates external interference and satisfies

[0025]

[0026] For any Represents a time variable.

[0027] Step 3: The H infinite lag formation control strategy with communication time delay is designed as follows:

[0028]

[0029] In the above formula, c = 1, 2, ..., l, l represents the number of agents in the multi-agent system, represents the control input of agent c, Represents controller parameters, and represent the position vector and velocity vector of agent c respectively, and denote the position vector and velocity vector of the virtual leader respectively, t is the time variable, represents an a-dimensional real vector, represents the time lag between agent c and the virtual leader, is the desired relative position between agent c and the virtual leader, is the desired relative position between agent i and the virtual leader, represents the communication delay between agents, and denote the position vector and velocity vector of agent i with time delay β, respectively. is the coupling weight matrix between agents. If there is communication between agent c and agent i, then otherwise also, represents an l×l dimensional real matrix, is a nonlinear function and satisfies the following inequality:

[0030] ||δ(t,o1,o2)-δ(t,o3,o4)||≤q1||o1-o3 || +q2||o2-o4||;

[0031] For any where q1 and q2 are positive constants.

[0032] Compared with the prior art, the present invention has the following beneficial effects: a multi-agent system H infinite lag formation control method with communication time lag is proposed; considering that each agent's acquisition of its own state information obviously lags behind the acquisition of the virtual leader's state information and the multi-agent system is affected by external interference and communication time lag, the present invention proposes a multi-agent system H infinite lag formation control method with communication time lag and external interference for the first time. From the implementation point of view, the present invention requires less computing resources and the required control amount is easier to obtain; the multi-agent system H infinite lag formation control method with communication time lag 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

[0033] Figure 1 This is a flowchart of the infinite-delay formation control method for a multi-agent system H with communication delay.

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

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

[0036] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and 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.

[0037] It is understood that the terms "first", "second", etc. used in this application may be used herein to describe various elements, but unless otherwise specified, these elements are not limited by these terms. These terms are only used to distinguish a first element from another element. For example, without departing from the scope of this application, a first xx script may be referred to as a second xx script, and similarly, a second xx script may be referred to as a first xx script.

[0038] Step 1: Construct the mathematical model of the multi-agent system with external interference as follows:

[0039] Formula (1)

[0040] In the above formula, and Represent the position vector, velocity vector and control input of agent c respectively, and They represent the derivatives of the position vector and velocity vector of the agent c, respectively, t is the time variable, represents an a-dimensional real vector, represents the internal dynamics of the agent, Indicates external interference and satisfies

[0041]

[0042] For any represents the time variable; is a nonlinear function and satisfies the following inequality:

[0043] Formula (2) ||δ(t,o1,o2)-δ(t,o3,o4)||≤q1||o1-o3||+q2||o2-o4||;

[0044] For any where q1 and q2 are positive constants.

[0045] The mathematical model of the virtual leader is expressed as follows:

[0046] Formula (3)

[0047] In the above formula, and represent the position vector and velocity vector of the virtual leader respectively, and denote the derivatives of the position vector and velocity vector of the virtual leader, respectively. represents the internal dynamics of the virtual leader, t is the time variable, represents an a-dimensional real vector.

[0048] Step 2: The multi-agent system supported by formula (1) can achieve H infinite lag formation if the following conditions are met:

[0049]

[0050] For any s1 represents the time variable, l represents the number of agents in the multi-agent system, where m is a normal number, and represent the position vector and velocity vector of agent c respectively, and represent the position vector and velocity vector of the virtual leader respectively, represents an a-dimensional real vector, represents the time lag between agent c and the virtual leader, and denote the position vector and velocity vector of the virtual leader with a time lag α, respectively. is the expected relative position between agent c and the virtual leader, V(·) is a non-negative function, represents a real number, Indicates external interference and satisfies

[0051]

[0052] For any Represents a time variable.

[0053] Step 3: The H infinite lag formation control strategy with communication time delay is designed as follows:

[0054] Formula (4)

[0055] In the above formula, c = 1, 2, ..., l, l represents the number of agents in the multi-agent system, represents the control input of agent c, Represents controller parameters, and represent the position vector and velocity vector of agent c respectively, and denote the position vector and velocity vector of the virtual leader respectively, t is the time variable, represents an a-dimensional real vector, represents the time lag between agent c and the virtual leader, is the desired relative position between agent c and the virtual leader, is the desired relative position between agent i and the virtual leader, represents the communication delay between agents, and denote the position vector and velocity vector of agent i with time delay β, respectively. is the coupling weight matrix between agents. If there is communication between agent c and agent i, then otherwise also, represents an l×l dimensional real matrix, is a nonlinear function and satisfies the following inequality:

[0056] ||δ(t,o1,o2)-δ(t,o3,o4)||≤q1||o1-o3||+q2||o2-o4||;

[0057] For any where q1 and q2 are positive constants.

[0058] Step 4: Definition and According to formulas (1), (3) and (4), we can get

[0059] Formula (5)

[0060] In the above formula,

[0061] E=diag(e1,e2,…,e l );

[0062]

[0063] A(t)=((θ k (t)) T ,(θ b (t)) T ) T ;

[0064] B(t)=(ε T (t),ε T (t-β) T ;

[0065]

[0066] In the embodiment of the present invention, if there is and a positive constant m such that:

[0067] Formula (6)

[0068] Formula (7)

[0069] In the above formula, and Then the multi-agent system provided by formula (1) can realize H infinite lag formation under the control strategy provided by formula (4).

[0070] For the error system provided by formula (5), the following Lyapunov functional is constructed:

[0071] Formula (8) From formula (2), we can get:

[0072] Formula (9) Formula (10) According to formulas (7), (9), and (10), we can get

[0073] Formula (11) In the above formula, v1=3q1+q2, v2=q1+3q2+2, and

[0074] Combining formulas (6) and (11), we can get

[0075] Formula (12)

[0076] In the above formula, and

[0077] According to formula (12), we can get

[0078]

[0079] For any s1 represents the time variable.

[0080] Therefore, the multi-agent system provided by formula (1) can realize H infinite lag formation under the control strategy provided by formula (4).

[0081] In order to facilitate those skilled in the art to better understand the technical solution of the present invention, examples are selected for simulation verification;

[0082] Consider the following multi-agent system with external disturbances:

[0083] Formula (13)

[0084] In the above formula, k c (t)=(k c1 (t),kc2 (t)) T , z c (t)=(z c1 (t),z c2 (t)) T , and denote the position vector, velocity vector, control input and external disturbance of the agent c respectively; δ(t,k c (t),z c (t))=(2sin(k c1 (t))-0.8z c1 (t),sin(k c2 (t))-0.2z c2 (t)) T Obviously, δ(t,·,·) satisfies the following inequality:

[0085] ||δ(t,o1,o2)-δ(t,o3,o4)||≤2.4||o1-o3||+1.5||o2-o4||;

[0086] For any Represents a 2D real vector.

[0087] choose and

[0088]

[0089] Using the YALMIP toolbox in MATLAB, we can obtain the following parameters to make conditions (6) and (7) true:

[0090] m = 0.8127;

[0091] E=diag(19.9427,19.8925,19.9640,20.0488,19.8925);

[0092]

[0093] Therefore, the multi-agent system provided by formula (13) can realize H infinite lag formation under the control strategy provided by formula (4). Figure 2 and Figure 3 They respectively describe the control strategy provided by formula (4) under the action of k c (t)-k * (t-0.8) and z c (t)-z * (t-0.8),c=1,2,…,5. Figure 2and Figure 3 It can be seen that as time goes by, the multi-agent system provided by formula (13) can achieve H infinite lag formation.

[0094] It should be understood that, although each step in the flow chart of the 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 strict order restrictions, 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.

[0095] 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 can 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).

[0096] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0097] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

[0098] The above description is only a preferred embodiment of the present invention and 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.

Claims

1. A multi-agent system H infinite delay formation control method with communication time delay, characterized in that: The method comprises: Construct a mathematical model of a multi-agent system with external interference and a virtual leader; Based on the mathematical model of multi-agent system and virtual leader, the error system is obtained; Design a H infinite-delay formation control strategy with communication delay; The corresponding Lyapunov functional is constructed to analyze and derive the conditions for the multi-agent system to achieve H infinite lag formation; The mathematical model of the multi-agent system with external interference is constructed as follows: In the above formula, and Represent the position vector, velocity vector and control input of agent c respectively, and Respectively represent the derivatives of the position vector and velocity vector of agent c, represents the internal dynamics of the agent, t is the time variable, represents an a-dimensional real vector, Indicates external interference and satisfies For any represents the time variable; is a nonlinear function and satisfies the following inequality: For any o1,o2,o3, Where q1 and q2 are positive constants; The control strategy of H infinite-delay formation with communication delay is designed as follows: In the above formula, c = 1, 2, ..., l, l represents the number of agents in the multi-agent system, represents the control input of agent c, Represents controller parameters, and Represent the position vector and velocity vector of agent c respectively, and denote the position vector and velocity vector of the virtual leader respectively, t is the time variable, represents an a-dimensional real vector, represents the time lag between agent c and the virtual leader, is the desired relative position between agent c and the virtual leader, is the desired relative position between agent i and the virtual leader, represents the communication delay between agents, and denote the position vector and velocity vector of agent i with time delay β, respectively. is the coupling weight matrix between agents. If there is communication between agent c and agent i, then otherwise also, represents an l×l dimensional real matrix, is a nonlinear function and satisfies the following inequality: ||δ(t,o1,o2)-δ(t,o3,o4)||≤q1||o1-o3||+q2||o2-o4||.

2. The control method of H infinite lag formation of a multi-agent system with communication time delay according to claim 1, characterized in that: The mathematical model of the virtual leader is: In the above formula, and represent the position vector and velocity vector of the virtual leader respectively, and denote the derivatives of the position vector and velocity vector of the virtual leader, respectively. represents the internal dynamics of the virtual leader, t is the time variable, represents an a-dimensional real vector.

3. The control method of H infinite lag formation of a multi-agent system with communication time delay according to claim 1, characterized in that: The H infinite lag formation is defined as follows: For any s1 represents the time variable, l represents the number of agents in the multi-agent system, where m is a normal number, and Represent the position vector and velocity vector of agent c respectively, and represent the position vector and velocity vector of the virtual leader respectively, represents an a-dimensional real vector, represents the time lag between agent c and the virtual leader, and denote the position vector and velocity vector of the virtual leader with a time lag α, respectively. is the expected relative position between agent c and the virtual leader, V(·) is a non-negative function, represents a real number, Indicates external interference and satisfies For any Represents a time variable.

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