Consistency Research Of Time-delay Multi-agent Systems Based On PI Control

Recently,multi-agent systems have attracted more and more researchers' attention because of their wide applications in distributed computing,sensor networks and robot formation.One of the most fundamental research topics in the coordinated control of multi-agent systems is the consensus problem.Consensus means that the state of each agent eventually converges to a common value over time.Consensus is achieved by designing a distributed control protocol,in which each agent only exchanges information with its neighboring agents.This paper designs a novel proportional integral(PI)control protocol to solve the consensus problem.In addition,due to the limitation of speed,there always exists communication delay in the transmission of information between the agents.Therefore,the research object of this paper is the multi-agent system with time delay.On this basis,this paper mainly studies the consensus problems of multi-agent systems with time-delay under directed topology based on PI control.The main contents are as follows:Firstly,the consensus problems of first-order and heterogeneous multi-agent systems with time-delay under directed topology are studied.A PI-like control protocol is proposed for the first-order multi-agent systems with time-delay.For the cases where the time-delay is constant and time-varying,sufficient conditions of consensus are given.The conservativeness of the sufficient conditions is reduced by increasing the triple integral term.Then,the simulations of numerical examples are given to verify the correctness of the conclusions.The results are extended to the case of heterogeneous multi-agent systems.Sufficient conditions of consensus are also given.Then,the consensus problems of time-delay multi-agent systems with nonlinear dynamics or disturbance under directed topology are studied.For these two cases,the PI control protocols are given,respectively.The sufficient conditions are obtained and the simulations of numerical examples are given to verify the correctness and effectiveness of the obtained conditions.In particular,advantages and disadvantages of control protocols based on proportional and proportional-integral are given by simulations of numerical examples for multi-agent systems with disturbance.Finally,the consensus problem of first-order directed multi-agent systems with timedelay based on distributed PID control is studied.The PI control protocol proposed in the previous two chapters is extended to the PID control protocol.And it is applied to the firstorder multi-agent systems with time-delay under directed topology.The sufficient condition of consensus is given and the simulation of numerical example is also given to verify the effectiveness of the proposed design method and the conclusion.