Leader-Following Consensus Control For Nonlinear Multi-Agent Systems Under Jointly Connected Topology

In recent years,the consensus of multi-agent systems has been a hot topic in many fields.While the dynamic equations of agents were usually limited to single integrator,double integrator or general higher-order linear systems in the existing research on asymptotic consensus.The study of multi-agent systems subject to unknown disturbance and nonlinearity needs to be strengthened.Another common problem is that most proposed distributed consensus protocols were based on an ideal condition,which the leader’s control input was zero or known.However,in most cases,this is not realistic.In addition,compared with asymptotic consensus,fixed-time consensus is more practical,and fixed-time control also has stronger anti-disturbance ability,higher control accuracy and so on.More importantly,fixed-time consensus can well solve the defect that the convergence time depends on the initial value in the finite time consensus.Therefore,on the basis of previous literatures,this dissertation uses Lyapunov stability theorem,fixed-time stability theory and adaptive control theory to study the asymptotic leader-following consensus control problem and fixed-time leader-following consensus control problem of nonlinear multi-agent systems under jointly connected graph.The specific work of this dissertation is as follows:(Ⅰ)Asymptotic consensus tracking control for nonlinear multi-agent systems under jointly connected topologyThe distributed tracking control problem of the nonlinear multi-agent systems with a leader is studied,and the multi-agent systems is subject to unknown disturbance,where the control input of the leader is non-zero and unknown.Based on the relative information(local information)between agents and the maximum eigenvalue and minimum eigenvalue of the Laplacian matrix(global information),a distributed controller with adaptive coupling gain is designed.In addition,considering that this problem is studied under the jointly connected graph,the stability of Lyapunov function is analyzed by Cauchy convergence theorem.Finally,simulation is used to prove the theory more intuitively.(Ⅱ)Fixed-time consensus tracking control for nonlinear multi-agent systems under jointly connected topologyThe fixed-time leader-following consensus problem for the nonlinear multiagent systems is researched,and this multi-agent systems is affected by unknown disturbances under the jointly connected graph.In order to achieve the control goal,a specific fixed-time consensus protocol is designed,which can include a specified item specifically to reject the influence of unknown external disturbances.Compared with other literatures on the fixed-time consensus problem of the multiagent systems,the advantage of this control protocol is that it can dominate the influence of the multi-agent systems nonlinearity and reject the influence of the external disturbance under the jointly connected graph,simultaneously.Finally,simulation example is given to prove the effectiveness of the theoretical results.Considering that in practical applications,information transmission between agents is often affected by terrain obstacles and external disturbance,which leads to the change of communication topology,this dissertation systematically studies the tracking control consensus of the nonlinear multi-agent systems under jointly connected graph according to the order from asymptotic consensus to fixed-time consensus.