Research On Fixed Time Consensus Of Nonlinear Multi-agent Systems With Perturbations

With the continuous development of modern science and technology,the research on group behavior has been paid more attention by many experts and scholars,and the cooperative control of multi-agent system is one of the heat spots of group behavior research.Multi-agent system is a large-scale complex system which is composed of a large number of autonomous or semi-autonomous subsystems with distributed configuration connected by network.An agent is a physical or abstract entity whose state quantity is affected by many factors such as internal structure,control input and external disturbance.In practical applications,most agents have nonlinear elements,and the system expects to achieve uniform convergence in a fixed time.Therefore,the problem of fixed-time consensus of nonlinear multi-agent system with disturbance is investigated,and the specific contents are as follows:Firstly,fixed time consensus problem for a class of nonlinear multi-agent systems with discontinuous dynamics and bounded perturbations is studied.For leaderless condition,a control protocol with auxiliary signals is designed for the highly nonlinear system.The original problem is transformed into the fact that the agent can successfully track the auxiliary signals and reach agreement by the auxiliary signals,so that the whole system can achieve the consensus.The designed auxiliary signal is not transmitted in the communication channel,which can effectively reduce the calculation cost of the system.Then,the corresponding control protocol is designed for the leader-following system,so that the agent can track the actual leader in the system after tracking the auxiliary signal successfully,and the consensus of leaderfollowing in fixed time is achieved.Secondly,the fixed time consensus problem of nonlinear stochastic multi-agent system under fixed topology and switching topology is investigated.A nonlinear control protocol is designed for a fixed topology to achieve fixed time consensus.Then,the conclusion is extended to the switching topology,and the corresponding control protocol is designed,so that the condition of system stability is independent of the dwelling time of the switching topology subgraph,and the union of the switching topology subgraph only requires to satisfy the connectivity condition to achieve the fixed time consensus,and the model is more general.Finally,by using non-smooth analysis,Lyapunov stability theory,algebraic graph theory and other theories,it is proved that the system can achieve fixed time consensus in any initial state,and the convergence time is independent of the initial state of the agent.meanwhile,the upper bound of the global stable convergence time of the system is derived.The validity of the theoretical results is further verified by simulation results.