Research On Fixed-time Consensus Of Multi-agent Systems

In the past ten years,the consensus problem of multi-agent systems(MASs)has become a key problem in the control field.In practical application,due to resource,cost and other reasons,we hope that the systems can achieve consensus in a certain time,and accelerate the convergence speed can improve the anti-interference and robustness of multi-agent systems.So how to achieve fast convergence becomes particularly important.Because of the complexity of the environment,we usually can't get the initial state,so how to realize fast convergence and find the explicit estimation that the convergence time is independent of the initial state becomes more important.Hence this paper will study the fixed-time consensus of multi-agent systems.1.Based on graph theory,fixed-time stability theory and Lyapunov stability,the fixed-time average consensus(FTa C)and fixed-time tracking consensus(FTt C)of multiagent systems are studied.In this text,we consider the fixed-time average consensus of the first-order multi-agent systems without leader,the fixed-time tracking consensus of the first-order multi-agent systems with a leader,and the fixed-time tracking consensus consensus of the second-order multi-agent systems with a leader,reasonable distributed control protocols are designed.By using Lyapunov's stability and other knowledge,the sufficient conditions for the fixed-time consensus of the systems are obtained,and the explicit estimation of the convergence time independent of the initial condition is given.2.Based on the theory of fixed-time stability and the characteristics of a special function,a reasonable distributed observer is designed.Secondly,two kinds of control protocols are designed by using observers.At last,by Lyapunov's stability and some common inequalities,a sufficient condition for the realization of the fixed-time tracking consensus of the hybrid order multi-agent systems and an upper bound of convergence time are obtained.3.Based on the basic knowledge of sliding mode control,Lyapunov stability and energy function,the fixed-time tracking consensus of general multi-agent systems and connectivity preserved are studied.In this paper,the first-order and second-order multiagent systems with a leader are studied.Using Lyapunov's stability,energy function,arc method and other basic knowledge,we obtain the sufficient conditions for the systems to achieve the fixed-time tracking consensus and connectivity preserved,and the explicit estimation of the convergence time that independent of the initial condition.