Containment-rendezvous Control Of Multi-agent Systems

Recently,the consensus problem of multi-agent systems has been an active research point in control theory,and it has widespread engineering application value in cooperative surveillance,sensor networks,spacecraft formation flying,etc.The aim of consensus problem is to let multiple agents reach a same final state by local communication and information exchange under the designed control protocol.The containment-rendezvous control problem researched in this paper is a special consensus problem with multiple leaders,and it requires that all followers can enter the convex spanned by leaders and reach a same final state under the appropriately designed control protocol.Therefore,the containment-rendezvous problem with several different kinds of multi-agent systems is discussed in this paper.The main contents of our work are listed as follows:(1)Containment-rendezvous control problem of first-order linear multi-agent system under directed topology is investigated,and a new containment-rendezvous control algorithm is proposed.Based on the conventional containment algorithm,a integral term is added to eliminate the state error.Using the generalized Nyquist stability criterion and the final value theorem,sufficient convergence conditions for followers achieving the containment-rendezvous are obtained under the general directed connected topology and symmetric connected topology respectively.Furthermore,it is proved that our proposed protocol drives the followers with unconnected topology to converge to the convex hull of the leaders by the same method.(2)Containment-rendezvous control problem of second-order multi-agent system under balanced connected topology is investigated.According to the proposed control algorithm for the first-order system,the containment-rendezvous control algorithm for second-order system is proposed.In order to simplify the parameter conditions,the vertexes defined as virtual leaders are added,and the closed-loop system can be seen as two parts through the analysis.On the basis of the frequency-domain analysis method,sufficient convergence condition is given to achieve containment-rendezvous under the balanced directed connected topology.(3)Containment-rendezvous control problem of second-order multi-agent system with multiple first-order leaders under directed connected topology is investigated.Since the first-order leaders are not able to provide the velocity information to second-order followers that is needed,the containment-rendezvous control algorithm is improved form the designed protocol for first-order system to insure the convergence of followers’ velocity.The sufficient convergence condition for the achievement of the containment-rendezvous for all followers is given by the analysis in frequency-domain.