CN113625559A - Multi-agent system cooperative control method based on specified time convergence - Google Patents

Multi-agent system cooperative control method based on specified time convergence Download PDF

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CN113625559A
CN113625559A CN202110855681.XA CN202110855681A CN113625559A CN 113625559 A CN113625559 A CN 113625559A CN 202110855681 A CN202110855681 A CN 202110855681A CN 113625559 A CN113625559 A CN 113625559A
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agent
agent system
consistency
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刘丹复
诸葛嘉锵
黄娜
陈张平
张帆
孔亚广
何中杰
张尧
郑小青
赵晓东
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Hangdian Haining Information Technology Research Institute Co ltd
Hangzhou Dianzi University
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Hangzhou Dianzi University
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Abstract

The invention discloses a multi-agent system cooperative control method based on specified time convergence. The method comprises the steps of firstly determining a multi-agent system set, establishing a communication network topological graph of the multi-agent system, secondly determining a first-order dynamic model of the multi-agent system, and then giving a multi-agent appointed time consistency control protocol and determining a cooperative consistency condition of the system based on the measurable state of the multi-agent system. And finally, writing the designed multi-agent consistency protocol into each agent through programming, and realizing the distributed information interaction among the agents through the established communication topological graph. The invention realizes the consistency of the appointed time of the first-order multi-agent system by designing the gain function, has the three advantages of presetting the convergence time upper bound, not depending on the initial state and having nothing to do with the control parameter, and can still meet other convergence performance requirements after the appointed time upper bound required by the control performance by designing the attribute function.

Description

Multi-agent system cooperative control method based on specified time convergence
Technical Field
The invention belongs to the field of computer science and control, and relates to a first-order multi-agent system distributed cooperative consistency control method based on specified time convergence.
Background field of the invention
In recent years, the research of multi-agent cooperative control has been remarkably advanced, more and more large-scale engineering tasks cannot realize multiple functions in the planning by only depending on single equipment or machines, and in scientific research of many subjects, the performance displayed by the system as a whole can have behavior characteristics different from the individual parts of the system.
The multi-agent control aims to enable a plurality of systems with simple intelligence and convenient management and control to realize complex intelligence through mutual cooperation, so that the system modeling complexity is reduced, and meanwhile, the robustness, reliability and flexibility of the system are improved. At present, a multi-agent system is widely applied to a plurality of fields such as traffic control, a smart grid, production and manufacturing, unmanned aerial vehicle control (formation), a sensor network, data fusion, multi-mechanical arm cooperative equipment and the like. Where the consistency problem and the control convergence rate are important concerns, researchers have proposed limited/fixed time strategies based on this concern, which depend on the initial values of the system and the controller parameters, which means that the design of the given time and controller parameters requires complex calculations in the early stages. In contrast, it is very challenging and valuable to design a multi-agent consistent controller protocol that converges at a given time, which can predict the convergence time of any given control system without calculation.
Disclosure of Invention
In order to solve the problems, the invention provides a distributed first-order multi-agent system consistency control method based on specified time.
The designated time consistency means that the multi-agent system realizes cooperative consistency in any designated time. Compared to finite time and fixed time consistency, the specified time policy has the following advantages: 1) independent of the initial state of the smart system; 2) independent of controller parameters; 3) any desired setting may be made.
The technical scheme adopted by the invention comprises the following steps:
step 1) determining a multi-agent system set, establishing a communication network topological graph G of the multi-agent system, and describing communication among agents by using a Laplace matrix L;
step 2) determining a dynamic model of the first-order multi-agent system.
And 3) giving a multi-agent appointed time consistency control protocol based on the measurable state of the multi-agent system.
And 4) determining a cooperative consistency condition of the system, which is mainly proved by Lyapunov stability theorem.
And 5) writing the designed multi-agent consistency protocol into each agent through programming, realizing distributed information interaction among the agents through the established communication topological graph, and realizing multi-agent cooperative consistency meeting the control performance requirement.
The invention has the advantages that a new control protocol with stable designated time is provided under the traditional consistency protocol, the consistency of the designated time of the first-order multi-agent system is realized by designing the gain function, the three advantages of preset convergence time upper bound, independence on the initial state and independence on the control parameter are achieved, and the attribute function is designed to ensure that the system can still meet other convergence performance requirements, such as exponential asymptotic, limited or fixed time convergence, after the designated time upper bound required by the control performance is reached.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the present invention comprises the steps of:
step 1) determining a multi-agent system set x ═ { x ═ x1,…,xnN represents the number of agents.
The multi-agent communication topology can be described as a connectionless graph G (V, E), where V ═ V { (V })1,…,vnAnd E respectively represent a set of agents and a set of communication edges between agents. For an undirected graph, the edge ∈i,jE represents that the ith agent and the jth agent can mutually transmit information, Ni＝{j|∈i,jE, j ≠ i } represents the communication neighbor set of the ith agent. In general, with adjacency matrix a ═ aij]∈Rn×nThe degree matrix D is formed by Rn×nAnd the Laplace matrix L ∈ Rn×nCommunication connection relationships are described. Wherein, when is ∈i,jE is E, aij>0, otherwise aij＝0；D＝diag{d1,d2,…,dn}，
Figure BDA0003184058770000021
Let L be D-A.
Step 2) determining a first-order dynamic model of the multi-agent system:
Figure BDA0003184058770000022
wherein xi(t)∈RmRepresents the state of agent i at time t, ui(t)∈RmRepresents the control input of the second agent i at time t; x (t) ═ x1(t),...,xn(t)]T，x0X (0) represents an initial state; for convenience of description, all the conclusions of the present invention can be extended to d when d is 1>1, the case;
and 3) giving a multi-agent appointed time consistency control protocol based on the measurable state of the multi-agent system.
Step 3.1) defining the measurable cooperative state of the ith agent at the time t as follows:
Figure BDA0003184058770000031
q (t) ═ q1(t),...,qn(t)]TQ (t) ═ lx (t);
step 3.2) designing a multi-agent consistency protocol:
ui(t)＝-γi(t)sign(qi(t))φ(|qi(t)|)
wherein gamma isi(t)>0 represents the time-varying gain function of the ith agent, which can also be understood as a timer function; sign (·) represents a sign function; phi (-) represents the attribute function.
Step 3.3), selecting an attribute function phi (| z |) ═ z |, and defining a timer function to have the following form:
Figure BDA0003184058770000032
wherein the control parameter epsiloni>0，ηi>0; w (t) represents a time-dependent auxiliary function and satisfies w (t) ≧ 0,
Figure BDA0003184058770000033
if so, the method comprises the following steps:
Figure BDA0003184058770000034
where T is the desired specified upper time bound
And 4) determining the stability condition of the system, which is mainly proved by Lyapunov stability theorem.
Step 4.1) taking Lyapunov function
Figure BDA0003184058770000035
Wherein
Figure BDA0003184058770000036
It is possible to obtain:
Figure BDA0003184058770000037
where η is min [. eta. ]i,i＝1,…,n}，ε＝max{∈i1, …, n, and V (T) ≦ V for the lyapunov function at time T*Wherein
Figure BDA0003184058770000041
Step 4.2) when t is>T, the switching attribute function is phi (z) ═ alpha zp+βzqAchieving a fixed time consistency, where α>0，β>0, p ∈ (0,1) and q>1; the fixed convergence time is expressed as
Figure BDA0003184058770000042
And 5) writing the designed multi-agent consistency protocol into each agent through programming, realizing distributed information interaction among the agents through the established communication topological graph, and realizing multi-agent cooperative consistency meeting the control performance requirement.

Claims (3)

1. A multi-agent system cooperative control method based on specified time convergence is characterized by comprising the following steps:
step 1) determining a multi-agent system set, establishing a communication network topological graph of the multi-agent system, and describing communication among agents by using a Laplace matrix;
step 2) determining a dynamic model of the first-order multi-agent system:
Figure FDA0003184058760000011
wherein xi(t)∈RmRepresents the state of agent i at time t, ui(t)∈RmThe control input of a second agent i at the time t is shown, and n represents the number of agents;
step 3) based on the measurable state of the multi-agent system, giving a multi-agent specified time consistency control protocol, which specifically comprises the following steps:
step 3.1) defining the measurable cooperative state of the ith agent at the time t as follows:
Figure FDA0003184058760000012
q (t) ═ q1(t)，...，qn(t)]TQ (t) ═ lx (t);
where L is Laplace matrix, L ═ D-A, D is degree matrix, A is adjacency matrix, and A ═ aij]∈Rn×n，NiRepresenting a set of communication neighbors of the ith agent;
step 3.2) designing a multi-agent consistency protocol:
ui(t)＝-γi(t)sign(qi(t))φ(|qi(t)|)
wherein gamma isi(t) > 0 represents the time-varying gain function of the ith agent; sign (·) represents a sign function; phi (-) represents an attribute function;
step 3.3), selecting an attribute function phi (| z |) ═ z |, and defining a timer function to have the following form:
Figure FDA0003184058760000013
wherein the control parameter epsiloni＞0，ηiIs greater than 0; w (t) represents a time-dependent auxiliary function and satisfies w (t) ≧ 0,
Figure FDA0003184058760000014
taking:
Figure FDA0003184058760000015
where T is a desired specified upper time bound;
step 4), determining the cooperative consistency condition of the system;
and 5) writing the designed multi-agent consistency protocol into each agent through programming, realizing distributed information interaction among the agents through the established communication topological graph, and realizing multi-agent cooperative consistency meeting the control performance requirement.
2. The multi-agent system cooperative control method based on specified time convergence as claimed in claim 1, wherein: the step 1) is specifically as follows:
determining a multi-agent system set x ═ { x ═ x1，…，xn}；
The communication topology of a multi-agent is described as a connectionless graph G (V, E), where V ═ V { (V)1，...，vnRespectively representing an intelligent agent set and a communication edge set between intelligent agents;
for an undirected graph, the edge ∈i，jE represents that the ith intelligent agent and the jth intelligent agent can mutually transmit information;
using adjacency matrix A ═ aij]∈Rn×nThe degree matrix D is formed by Rn×nAnd the Laplace matrix L ∈ Rn×nDescribing communication connection relation when being belonged toi，jE is E, aij> 0, otherwise aij＝0；D＝diag{d1，d2，...，dn}，
Figure FDA0003184058760000021
3. The multi-agent system cooperative control method based on specified time convergence as claimed in claim 1, wherein: and 4) determining the stability condition of the system, which is mainly proved by Lyapunov stability theorem.
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