Research On The Sampling And Fixed-time Consensus Control Of Multi-agent Systems

One of the main research directions of multi-agent system is consensus control.This paper focuses on the sampling consensus control and fixed-time consensus control of multi-agent systems.In practical application,due to the wide use of computer control system,sampling control strategy has gradually become an important control method in industrial production,and has almost replaced the traditional mechanical control methods.Therefore,this paper first studies the sampling consensus control of multi-agent systems.Secondly,considering the superiority of the fixed-time control strategy in estimating the stable time of dynamical systems,that is,the stable time is independent of system's initial states,many scholars have applied this method to the control of multiagent systems.However,this method has not been well applied to the consensus control of general linear multi-agent systems.Therefore,this paper also considers the fixed-time leader-follower consensus control of general linear multi-agent systems.In this paper,we first discuss the influence of sampling interval on the consensus of multi-agent systems when the communication structure(expressed as graph,so it is also called communication graph)is fixed and strongly connected.This paper points out that the stable sampling period of the single integrator system is closely related to the eigenvalues of the Laplace matrix corresponding to the communication graph matrix.It is also pointed out that the steady state of the system can be uniquely determined by the initial state of the system and the Laplace matrix corresponding to the communication graph matrix when the communication graph is fixed and strongly connected.Secondly,this paper further discusses the influence of sampling interval on system consensus in multi-agent system with switched and non strongly connected communication structure.This paper points out that if there is a time partition such that the joint graph of the system's communication graphs in each partition is a strongly connected graph,then the multi-agent system can also achieve sampling consensus.When it is coming to the leader-follower consensus control of general linear multiagent systems,we first study the fixed-time observation problem of the general linear multi-agent system.By introducing an auxiliary matrix,a fixed-time observer for followers' states of the system is designed.In addition,the auxiliary matrix can also increase the accuracy of the estimation of observer's stable time.Then,an auxiliary matrix is used to design the fixed-time controller.The parameters of the controller can be obtained by solving a matrix inequality,which is very helpful for engineering calculation.Through demonstration,this paper points out that the designed fixed-time controller can not only ensure the leader-follower consensus of the system in a fixed time,but also increase the accuracy of the estimation of observer's stable time.All the theories in this paper are verified by numerical simulation,and the results are mostly presented in pictures,and the results further support the correctness of the theory.