The Consensus Of Multi-agent Systems With Switching Topologies

Recent years,with the development of theory and technology,multi-agent systems have been widely used in many fields.As the basis of coordinated control analysis,the consensus problem has been widely concerned by researchers at home and abroad.However,most existing results only considered the consensus problem under homogeneous systems or fixed topology.However,in actual physical systems,the topology may change due to the disruption or recovery of communication between agents,and the dynamics of agents may also be different.Therefore,studying the heterogeneity of systems and switching topologies are more in line with the actual system requirementsIn this paper,we consider the heterogeneous multi-agent systems with switching topologies.Based on graph theory,linear matrix inequalities and Lyapunov stability theory,the problems of the quasi-consensus,the group-bipartite consensus and the quasi-group-bipartite consensus of the system are studied in depth.The main works are as follows:1.For first-order heterogeneous nonlinear multi-agent systems,the quasi-consensus of system with a leader is studied.The topologies are constantly switched between cooperation and competition.The system parameters are switched combined with Markov processes.When the total time of the topology in the cooperative relationship meets certain conditions,based on Lyapunov stability theory and La Salle invariance principle,the conditions for parameters when the multi-agent systems achieve quasi-consensus are given,and the upper bound of the error is calculated.Without considering the nonlinear term,the conclusion is extended to linear heterogeneous multi-agent systems.2.For mixed-order heterogeneous multi-agent systems with first-order and second-order agents,the group-bipartite consensus is investigated.Considering both pinning control method and event-triggered mechanism,only when the in-degree of agent is zero,the agent is pinned.According to the order of the agent and whether it is pinned,the appropriate triggering rules are designed.On the basis of theoretical analysis,the sufficient conditions for group-bipartite consensus of systems under switching topologies are given.It is also proved that there is no Zeno behavior in the convergence of the system.The numerical simulation results show that group consensus and bipartite consensus are special cases of the group-bipartite consensus.3.For first-order heterogeneous nonlinear multi-agent systems,the quasi-group-bipartite consensus with multiple leaders is studied.Firstly,the definition of quasi-group-bipartite consensus is given by combining the concepts of quasi-consensus and group-bipartite consensus.When the topological graphs are structurally balanced,by graph theory and Lyapunov stability theory,it is proved that the system under switching topologies can achieve quasi-group-bipartite consensus when the parameters meet certain conditions.The conclusion is extended to linear heterogeneous systems.The correctness of the conclusion is verified by numerical simulation,and the quasi-group-bipartite consensus in several special cases are simulated.