Bipartite Tracking Consensus Of Linear Multi-agent Systems With A Leader

In recent years,applications related to multi-agent systems can be seen everywhere in many fields.Among them,collaborative control is a research hotspot for most experts and scholars.In this field,the research of consistency is its focus.With that,the bipartite tracking consensus of linear multi-agent systems has also become the hot topic of academic circles.In practical application,for the sake of fulfilling some special tasks,the leader should have some non-zero control actions.On the other hand,in many real applications,the interaction topology among the agents should be ticketed as a directed graph.on this basis,this paper mainly studies the bipartite tracking consensus of linear multi-agent systems with a dynamic leader under signed digraph.Firstly,to solve the problem of the bipartite tracking consensus in multi-agent system based on directed communication topology,a mathematical model of the system is established.Then a static consensus protocol was designed,by constructing the Lyapunov function,applying the La Salle's invariance principle,matrix theory,the graph theory and the algebraic Riccati inequality(LMI),so that the bipartite tracking consensus are obtained.At last,the simulation results can illustrate the validity of this theory.Secondly,in general,when the scale of multi-agent systems is large,due to some reasons,the global information cannot be fully obtained.At this time,there are some limitations in using static consensus protocol.So as to make improvements and propose a new fully distributed consensus protocol,which only needs to obtain local information.By designing an appropriate Lyapunov function and applying the knowledge of the algebraic Riccati inequality(LMI),the Lasalle invariance principle and graph theory,it is verified that the designed fully distributed consensus protocol can make the bipartite tracking consensus of linear multi-agent systems under certain conditions.Finally,the validity of the theory is verified by simulation experiments.