Fixed-time Bipartite Consensus For A Class Of Multi-agent Systems

Nowadays,the number of researcher who have studied the coordinated control of multi-agent systems(MASs)is on the increase.As a crucial topic of MASs,coordinated control has received extensive attention from many scholars.In practical applications,it is obviously impossible for all individuals to have only a cooperative relationship.It is more meaningful to study a MAS that has both cooperative relationship and antagonism relationship.On the basis of the above two relationships,the bipartite consensus of MAS is proposed.In order to prevent the MAS from being affected by the initial values,the first-order MAS fixed-time consensus is proposed in the existing works.However,this article studies the bipartite consensus of a class of MASs at a fixed-time.Firstly,consider the second-order MAS,consisting of a leader and N followers,and study its fixed-time bipartite consensus problem.Secondly,a exquisite fixed-time control strategy is devised,and the stability of the system is checked by constructing a Lyapunov function,so that the system can achieve the fixed-time bipartite consensus.Finally,some simulations show that the effectiveness of the theoretical results.This paper also studies the multi-agent system with multiple leaders.For the sake of solving the containment control problem of the second-order MAS with multiple leaders,the containment control law is designed,and the Lyapunov function is also constructed.The related stability theory realizes the fixed-time bipartite containment control of the second-order MAS when the symbol graph is Euler’s directed graph.Finally,a simulation example is given to testify the feasibility of the proposed protocols.