Research On Fixed-time Consensus Of A Class Of Nonlinear Multi-agent Systems

Nowadays,the research on multi-agent systems has been receiving increased attention from the fields of mathematics,control theory,and systems science.As one of the basic problems of this topic,the consensus control is to design control protocols through local information to realize the collective behavior,and its purpose is to make the system reach the consensus.However,existing works show that the time taken for the system to reach the consensus is often influenced by the initial state.To overcome this challenge,this paper focuses on the fixed-time consensus problem of a class of nonlinear multi-agent systems.First of all,considering a nonlinear multi-agent system with a leader.Based only on the relative information of neighboring agents,a distributed control protocol without absolute values is designed.Subsequently,a Lyapunov function is constructed to analyze the stability.The time upper limit for the system to reach consensus is calculated by using the fixed-time consensus theory.Furthermore,when the selected parameters and the communication topology remain unchanged,the system can reach the consensus within the expected time regardless of how the initial conditions are changed.Finally,a numerical simulation is given to verify the feasibility of the conclusion.Secondly,the paper addresses the leaderless fixed-time consensus of nonlinear multi-agent systems.By selecting appropriate parameters,a fixed-time control protocol is developed.A Lyapunov function is constructed to analyze stability.The time upper limit for the system to achieve the consensus is calculated by using the fixed-time consensus theory,and the time upper limit is only related to the selected parameters and communication topology.Finally,a numerical simulation is conducted to verify the feasibility of the results.