Study On Event-triggered Consensus Problem Of Multi-agent Systems

With the rapid development of morden control technology and the indepth study of complex dynamic systems,the coordinated control of multi-agent systems has received much attention of many researchers,and the related research results have been widely used in wireless sensor networks,distributed control,UAV formation control,mobile intelligent robots,traffic control and other fields.As a particular focus of multi-agent cooperation,the consensus problem is mainly to study how to design an appropriate protocol or control law with which the state of each agent can converge to a same value based on local information exchange between individuals in the system.However,under the traditional consensus protocols,the multi-agent systems achieve consensus need a great number of information exchange between individuals,and require the systems to be equipped with high-performance hardware devices.In order to effectively reduce the information exchange between agents and reduce the system requirements for hardware devices,in this thesis,we will introduce the event-triggered control strategy into the consensus problem of multi-agent systems.On the basis of the existing research results,this thesis studies the consensus problem of multi-agent systems based on event-triggered control by using the algebraic graph theory,matrix theory,stability theory and other knowledge.The main contents of the dissertation are summarized as follows:Firstly,this thesis studies the leader-following consensus problem of the first-order multi-agent systems based on the event-triggered control.Two different event-triggered consensus control protocols,i.e.,centralized event-triggered control protocol and decentralized event-triggered control protocol are proposed.In the former,a global state error threshold is seted for all agents in the system,when the system error reaches the seted error threshold,all agents trigger events at the same time,meanwhile,update and pass their own sampling information.In the latter,for each agent it sets a state error threshold based on its neighbors' state,when the state error of the agent reaches the seted threshold,the agent independently triggers event and carries out the control task.Theoretical analysis shows that,under the two given event-triggered control protocols,the system can both achive the leader-following consensus,and there is no Zeno phenomenon.The simulation results verify the validity of the theoretical analysis.Secondly,based on the decentralized event-triggered control strategy,this thesis studies the average consensus problem of the second-order multi-agent systems.We decompose the state of all agents in the system into an average state and a non-uniform state deviating from the average,by using the model transformation method,the average consensus problem of the system is turned into the stability of the closed-loop system,and by using the matrix theory and Lyapunov stability theory,some sufficient conditions of the asymptotic stability of the system are given.Based on the stability theory we obtain the conclusion that the system can achieve the average consensus with the given event-triggered control protocol.Similarly,theoretical calculation shows that under the proposed scheme,Zeno behavior does not exist in the systems.Simulation results demonstrate the effectiveness of the theoretical results.Thirdly,in view of the shortcomings of the existing event-triggered control strategies,we propose an improved event-triggered control strategy.With the proposed strategy,each agent samples its neighbors' information and updates the controller only at its own triggering instants,it is not necessary to take into account its neighbors' event triggering instants.Based on the proposed event-triggered control strategy,the consensus problem of the second-order multi-agent system under the fixed and switching topologies is studied.we design an event-triggered consensus controller and give some consensus judgment conditions.Through theoretical analysis,we can get the following conclusions that whether in the fixed topology or the switching topology,the system can both achieve consensus with the given event-triggered control protocol if the topology of the system keeps strongly connected constantly,and Zeno behavior does not exist in the system.Simulation results exhibit that,compared with the existing event-triggered control methods,the improved event-triggered control method can effectively reduce the information exchange between agents and lower the system control signal update frequency,and thereby effectively save the network and computing resources of the system.Fourthly,based on the improved event-triggered control strategy above,we study the leader-following consensus problem of the second-order multi-agent system.It assumes that the leader is globally reachable,and only send its signal to the followers who are directly connected to it.By using the model transformation method,the leader-following consensus problem of the second-order multi-agent system is transformed into the stability problem of the closed-loop system,and sufficient conditions of asymptotic stability of the system are given by using matrix theory,Lyapunov stability theory and linear matrix inequality(LMI)method.Theoretical analysis shows that,as long as the system's communication topology contains a spanning tree,and the leader is the root node,then the system can reach the leader-following consensus under the given event-triggered control protocol,and Zeno phenomenon will not occur.A simulation example is given to verify the correctness of the theoretical analysis.Finally,this thesis studies the consensus problem of general linear multi-agent systems,a novel periodic event-triggered control method is proposed,and based on the proposed periodic event-triggered control method,the consensus protocol of the system is designed.By defining virtual delay,the consensus problem of the system is transformed into the stability problem of a class of time-varying delay system.By constructing Lyapunov-Krasovskii functional method,some sufficient conditions which ensure the system can reach asymptotic stability are obtained,and based on the stability criteria we further get the conclusion that the multi-agent system can achieve consensus under the given event-triggered control protocol.Algorithm analysis shows that,with the new event-triggered control strategy,each agent in the system does not only update the control input at its own triggering instants,but also ensures that the interval between any two consecutive event triggering instants is to be at least a given sampling period,so as to avoid the occurrence ofZeno.Numerical simulation shows the feasibility and effectiveness of the proposed method.