Research On The Impulsive Consensus Of Fractional-order Multi-agent Systems

With the increasing complexity of social environment,it is found that some physical sys-tems show fractional-order characteristics.Therefore,using fractional differential equations to analyze systems in complex environment is closer to practical significance.Fractional-order control system is a further extension of the traditional integer-order system.In the field of con-trol science research,fractional-order control system is not only a focus,but also a difficulty.This paper focuses on the unity of fractional-order multi-agent systems.Fractional multi-agent systems are multi-agent systems with fractional differentiation in the dynamic model of multi-agent.They belong to the expansion of traditional integer-order multi-agent systems.Con-sensus problem is a branch of coordinated control problem and the most basic problem in the research of multi-agent systems.Its purpose is to make all agents achieve the desired state by designing algorithms or protocols.With the help of fractional calculus theory,graph the-ory,Lyapunov stability theory and impulsive differential equation theory,this paper focuses on the consistency problems with event-triggering,time delay and finite time.The sufficient conditions for the impulsive consensus of fractional multi-agent systems are given,and the ef-fectiveness of the results are verified by numerical simulation.The main contributions of this paper are as follows:1.Using two kinds of pinning rules and event-triggered impulsive control methods,the consensus of fractional order multi-agent systems is studied.Compared with the fixed pinning technology in the existing literature,two pinning rules are considered here(i.e.randomly selected traction and orderly traction according to the distance of error state,hereinafter referred to as distance ordered pinning),and the agent is variable at each impulsive instant.On the basis of revealing the relationship between impulsive gain,impulsive controller and system order,this paper further discusses how to design an appropriate impulsive controller to adapt to different fractional-order multi-agent systems.At the same time,the sufficient conditions for system consensus and avoiding Zeno behavior are obtained.2.Using the distance ordered pinning rule and impulsive control methods,the quasi con-sensus problem of fractional-order multi-agent systems with time-varying delays is studied,in which there are both internal and external coupling delays.Sufficient conditions for quasi consensus are obtained by using Lyapunov Razumikhin method.The results show that the con-trol gain depends not only on the impulsive gains,but also on different fractional multi-agent systems,and the error bound of any agent can be maintained in a certain range in a small area determined by the boundary of external interference.3.The distance ordered pinning rule and impulse control methods are applied to a group of antagonistic coupled fractional-order multi-agent systems to achieve finite time dichotomy consensus.With the help of fractional calculus theory,Lyapunov stability theory and finite time consensus theory,the sufficient conditions for the dichotomy consensus of leader and follower are given.Compared with the existing results,the effect of impulsive control depends not only on the order of the system,but also on the impulsive gain.