Study On The Impulsive Consensus Of Nonlinear Multi-agent Systems

Since the 1980 s,multi-agent systems as the main research object in the field of distributed artificial intelligence have attracted more and more attention in the academic community,Related research results are widely used in many engineering fields.The basis of the multi-agent system is the distributed coordination and cooperation ability among the agents,and the consensus problem is the key to the distributed coordination and cooperation control of the agent.At the moment,the impulsive control method has the advantages of small control,high efficiency and low cost.It has been widely used by researchers and studied in depth.In general,the multi-agent system in practical applications will have the following problems: the system is a second-order or higher-order nonlinear system,there is a time-varying delay in the communication between the agents,there have a leader agent in the system,and the system network topology is dynamically switched,there are multiple clusters in the system,and so on.Therefore,research on the impulsive consensus of multi-agent systems based on the above problems undoubtedly has important theoretical and practical value.Based on the above consideration,a new impulsive control protocol is designed in this paper.On the one hand,the leader-following consensus of the second-order nonlinear multi-agent system is studied.On the other hand,the cluster-delay consensus in first-order nonlinear multi-agent system is studied.According to algebraic graph theory,impulsive differential equation theory,Lyapunov stability theory,matrix theory,Halanay inequality,Kronecker product and other related theories and lemma,the sufficient conditions for system impulsive consensus under certain assumptions are given.Finally,the results of the research in the paper are verified by the simulation of Matlab software.The research work of this paper is briefly described as follows:(1)With the conditions of active leadership and system topology switching,the leader-following consensus in the second-order nonlinear multi-agent systems is studied.The impulsive control protocol takes continuous control at non-pulsed moments and take discrete control at pulse moment,an innovative view was raised that the speed incrementof each agent is not only related to the displacement state of the adjacency agent but also to the velocity state.Constructing a New Model of Error System,based on Lyapunov stability theory,using mathematical induction and other related knowledge,get the sufficient conditions to achieve consensus when the system topology is directed and connected,and the result is verified by the Matlab simulation.(2)This paper studied the consensus of multi-agent systems with uncertainties and randomly occurring nonlinearities and impulsive input delay via impulsive control with topology switching.In the traditional protocol,it is usually assumed that the communication delay between adjacent individuals is the same as the communication delay between individual and leader,but this is conservative.In the fourth chapter of the new impulsive control protocol,the size of delay above can be different.Compared with traditional research methods,the approach that deals with the delay in complex network synchronization research is introduced into the research of consensus of multi-agent systems.Based on a generalized Halanay inequality,two sufficient conditions are given to meet the leader-following consensus of systems with topology switching,in other words,the delay does not affect the final consensus of system when the relevant parameters satisfy the theorem's conditions.Compared with the decision conditions with delay on other methods,the results of this study are less conservative,and the result is verified by the Matlab simulation.(3)For the first-order nonlinear multi-agent system with multiple clusters,the cluster-delay consensus is studied.Among them,the control protocol has the following innovations: First,the use of impulsive control to achieve cluster-delay consensus,reduce the cost of control and improve the control efficiency;Second,each agent not only receives both adjacent individuals in the same cluster but also receives status information of neighboring individuals in other clusters to update its current status.Based on algebraic graph theory,Lyapunov stability theory,impulsive differential equation theory,and so on.Two sufficient conditions are given to meet the cluster-delay consensus of systems.Finally,the result is verified by the Matlab simulation.