Consensus Of Multi-agent Systems With Input Delay

With the rapid development of science and technology,the problems of industrial production are becoming more and more large and complicated,and some large and complex problems can be achieved through the coordinated and coordinated implementation of multiple agents,so the distributed control of the multi-agent systems has become the focus of scholars in recent years.Based on information interaction between each agent and neighbor agent,the consensus problem is that the design consensus protocol makes all agents eventually reach the same state.An actual multi-agent system,when the agent receives the neighbor agent information,the reaction time and calculation speed will cause time delay,and the time delay has an important impact on the stability of the system.Therefore,dealing with time delay has important practical significance.This paper mainly studies the consensus problem of multi-agent systems with input delay,mainly from the following aspects:(1)The problem of the leader-follower consensus disturbance rejection under the directed network with fixed topology for a class of multi-agent systems with input delay and exogenous disturbances is discussed.Firstly,for the multi-agent systems with exogenous disturbances,a distributed state observer is given to estimate the state and disturbance simultaneously;Secondly,based on the truncated prediction approach,a consensus protocol is proposed for each agent by utilizing the estimated state and its own disturbance estimate information,which are obtained by using the relative output information between neighbors;Finally,sufficient conditions for the consensus of the multi-agent systems are constructed by using Lyapunov-Krasovskii theory.(2)The problem of the consensus under the directed network with fixed topology for a class of high-order Lipschitz nonlinear multi-agent systems with input time-varying delays is discussed.Firstly,when the multi-agent systems without time-varying delays,a consensus protocol is proposed for each agent,then sufficient conditions for the stability of the multi-agent systems are constructed by using Lyapunov theory and graph theory;Secondly,the prediction systems are obtained based on a future state prediction,the consensus protocol is extended to achieve the state consensus of the prediction high-order Lipschitz nonlinear multi-agent systems with time-varying delays;Finally,a simulation example is given to demonstrate effectiveness of the results.(3)The problem of the leader-follower consensus under the undirected network with fixed topology for a class of parametric uncertainties multi-agent systems with input time-varying delays is considered.Firstly,when the multi-agent systems without time-varying delays,the robust consensus control protocol is proposed for each parametric uncertainties agent;Secondly,the distributed prediction systems are presented based on state error information of the neighboring agents,then sufficient conditions for the stability of the prediction systems are constructed by using Lyapunov function and the robust consensus protocol is extended to achieve the state consensus of the prediction multi-agent systems with time-varying delays;Finally,the feasibility of the proposed method is verified.