Research On Consensus Problem Of Second Order Multi-agent Systems Under Heterogeneous Topologies

With the advent of the information age,the rapid development of Embedded technology and communication technology,giving the software platform and hardware foundation to the realization of the cooperative control of multi agent system.Multi-agent system has become a hot research topic with its good robustness and universality.Multi-agent cooperative control has been widely used in biological network systems,Unmanned Aerial Vehicle formation control,complex networks,distributed optimization computing and other fields.One of the core problems of multi-agent cooperative control technology is the consensus problem of multi-agent system,which goal is to make the state of the agents in the same system reach consensus in limited time.In this paper,we study the consensus of the second-order multi-agent system under heterogeneous topologies,and propose new algorithms for the consensus of heterogeneous topology of continuous systems.The problems are belong to the problem of consensus of multi-agent systems: time delay,nonlinear dynamical systems,leader-following.The contents and contributions of this paper are as follows:(1)A uniform control algorithm for the second-order multi-agent system under heterogeneous topologies with continuous time-delay is proposed.The heterogeneous topologies are used to describe the communication relationship between the position signals and the speed signals in the system.The sufficient conditions for the consensus are obtained,and the conclusion is verified by simulation.As the problem of time delay is widespread in communication systems,it is of great significance to solve the problem of time delay.In this paper,the classification problem of time-delay is introduced,then the consensus problem based on the general time-delay system is presented.The sufficient conditions for the consensus of the multi agent system are given.First,the reason why the delay problem of general systems is given is that,in order to better introduce the time-delay problem in heterogeneous topologies.Although there is no analysis about distinction between ordinary topologies and heterogeneous topologies.The algorithm has laid a foundation about the consensus of the multi agent system under the heterogeneous topologies.(2)Consensus algorithms for second-order multi-agent systems with nonlinear dynamic under heterogeneous topologies is proposed.Through the transformation of the system dynamics model,the consensus problem of the nonlinear multi-agent system is transformed to discuss the stability of the nonlinear system.Finally,the stability of the system is proved by designing Lyapunov function.In this paper,we discuss the problem of consensus of the system based on the undirected topology and improve the results of the previous research about the consensus problem of the nonlinear second-order system,so the research of the paper is innovative.Two control algorithms for different control targets are proposed,which are the consensus problem with non-zero convergence and zero convergence rate respectively.The sufficient conditions are given for the consensus problem of the multi agent system.Finally,through simulation,we verify the correctness of our conclusions.(3)In this paper,the communication topology discussed in this paper is a connected undirected graph for the convenience of the proof of stability of system.The connected undirected graphs with the corresponding Laplace matrix is symmetric.In this system,the state of the leader is time-varying.Based on the analysis of the consensus problem,the construction of the system model,the design of the controller and the design of the observer,the consistency analysis is made.Under the controller and observer,The problem of consensus of multi agent system is transformed into the research about system stability.The common Lyapunov function(CLF)is proposed,and give the sufficient Conditions that second-order multi-agent system under heterogeneous topologies with a leader.Finally,the simulation results show that the states of agents will reach the consensus under the controller and observer.