Research On Formation Of Multi-agent Systems Based On Complex Laplacian

In recent years,formation control,as one of the most actively researched topics within the realm of multi-agent systems has attracted wide attention of researchers.In this thesis,event-triggered similar formation control of multi-agent systems is investigated using complex-valued Laplacian.The major research content is the formation problem of multi-agent system based on the first-order differential and difference equations,respectively,and its application to the cluster formation.Firstly,similar formation of multi-agent systems by event-triggered control is studied.Continuous-time and discrete-time models are considered,respectively.The dynamic of each agent is described by complex-valued differential or difference equations.The distributed event-triggered control strategy is designed.The designed controller does not use global information.The triggering instants for each agent are determined by certain events that depend on the states of its neighboring agents.Continuous updating of controllers and continuous communication among agents are avoided.The obtained results show that multi-agent systems can globally exponentially reach a similar formation only using local information.Continuous communication among neighboring agents and continuous update of controllers are avoided.Furthermore,it is shown that the closed-loop system does not exhibit the Zeno behavior for the continuous-time dynamics case or the Zeno-like behavior for the discrete-time dynamics case.Secondly,similar formation of first-order continuous-time multi-agent systems with communication time delays is considered.The event-triggered controller with time delays is designed for each agent.The triggering function is designed,which depends on the state information of agents and exponential decay term.Multi-agent systems with communication time delays can globally exponentially reach a similar formation of target formation under the assumption that the interconnection graph of the multi-agent systems is 2-rooted.Moreover,Zeno behavior of closed-loop system is excluded.Furthermore,a simulation example is given to illustrate the efficiency of the proposed distributed event-triggered control strategy.Finally,similar formation of first-order multi-agent systems with continuous-time dynamics under event-triggered control is applied to cluster formation.It is obtained that the multi-agent system under event-triggered control can globally exponentially reach a similar cluster formation and Zeno behavior of closed-loop system is excluded.