Observer-based Prescribed-time Consensus Of Multi-agent Systems

In the past decade,multi-agent system has attracted considerable attention of many scholars due to its wide applications in the fields of unmanned technology,formation control,flocking,sensor network and so on.As one of the basic problems in the research of multiagent systems,consensus has played an important role in the practical systems applications and control theory researches.In recent years,with the traditional asymptotic stability,finitetime consensus and fixed-time consensus proposed and the increase of practical engineering requirements,prescribed-time consensus has been proposed and has its unique advantage,that is,the convergence time of multi-agent systems can be predetermined in physical allowable range and has nothing to do with initial values and system parameters.In addition,in practical engineering applications,the full states of all the agents are usually hard to be obtained directly or even unavailable.In order to overcome this difficulty,the state observers are introduced to effectively estimate the actual state of the agents.Based on the related works,this paper has further explored and analyzed the observer-based prescribed-time consensus of multi-agent systems.The effectiveness of the conclusions is confirmed by simulation verifications.The main works of this paper are summarized as follows:(1)The prescribed-time group consensus of single integrator multi-agent systems is investigated.According to whether the state of the agents are available,novel prescribed-time control protocols are designed,respectively.The sufficient conditions are established to realize prescribed-time group consensus under both undirected connected topology and directed topology containing a directed spanning tree with root node as the leader by using algebraic graph theory,Lyapunov stability and matrix theory.(2)In the research of prescribed-time group consensus of linear multi-agent systems,state observers are introduced to effectively estimate the actual state of the agents when they are unavailable.Moreover,the observer-based prescribed-time control protocols are designed for undirected connected topology and directed topology containing a directed spanning tree with root node as the leader.Based on linear system theory and other related knowledge,the sufficient conditions for linear multi-agent systems to realize prescribed-time consensus are obtained.(3)The concept of prescribed-time group output consensus for nonlinear multi-agent systems is proposed.Then,the problems of prescribed-time group output consensus with external disturbance or not are analyzed for the case of the state of the agents are unavailable.According to algebraic graph theory,nonlinear system theory,Lyapunov stability theory and matrix theory,the sufficient conditions of prescribed-time group output consensus for nonlinear multi-agent systems are derived by designing the observer-based prescribed-time control protocols.