Finite-time Consensus And Distributed Optimization For Several Classes Of Nonlinear Multi-Agent Systems

With the development of science and internet,control theory has evolved from the study of traditional single system to the modelling and control of more complex system.In recent years,multi-agent systems,as an important part of complex system,have received much attention due to its wide application in engineering.The basic problem of multi-agent systems which is called consensus problem is to design a distributed algorithm such that all the states of agents converge to a desired common value.The optimization problem of multi-agent systems is represented as a distributed optimal control problem.By giving the objective function of the single agent or the whole system,a distributed control protocol is not only to make the states of multi-agent converge to a desired common value,but also to minimize the objective function.At present,the optimal control of smart grid and formation control of aircraft can be modeled as multi-agent systems,and the corresponding distributed optimization problems have been investigated.In the physical and engineering environment,nonlinear dynamics always exist in the system and control goals need to be completed in a finite time.Therefore,it is of great theoretical significance and application value to study the finite-time consensus control of nonlinear multi-agent systems.This paper focuses on the finite-time consensus problem of several classes of nonlinear multi-agent systems under fixed topology,switching topologies and distributed optimization functions,including the following aspects.Firstly,we investigate the adaptive finite-time leader-following consensus problem of second-order nonlinear multi-agent systems with switching topologies.In the presence of unknown parameters and switching topologies,the finite-time consensus problem of the multiagent systems can be formulated as the adaptive finite time control of switched systems.This paper attempts to derive the stability condition of switched systems in terms of practical finitetime Lyapunov stability theory and average dwell time method.After that,a new adaptive finitetime distributed consensus algorithm is proposed to drive the consensus error to converge to a small neighborhood of the origin in finite time.Numerical simulations are presented to illustrate the effectiveness of the theoretical results.Secondly,we study the leaderless consensus problem with distributed optimization functions for the same class of second-order nonlinear multi-agent systems under fixed topology.Based on above distributed optimization problem,we construct the penalty function and propose a new adaptive finite-time distributed algorithm to drive the gradient function of penalty function converge to a small neighborhood of the origin in finite time under fixed penalty factor.By magnifying the penalty factor,the states of all agents will converge to the optimal solution.And we use the integrator technique to extend second-order multi-agent system to high-order multi-agent systems.Numerical simulations are presented to illustrate the effectiveness of the theoretical results.Finally,we focus on the leaderless consensus problem with distributed optimization functions of a class of nonlinear multi-agent systems under switching topologies.Similarly,we construct a penalty function.Based on the gradient method,a new adaptive distributed algorithm is proposed such that the gradient function of penalty function will converge to a small neighborhood of the origin in finite time under switching topologies.Magnifying the penalty factor,the states of all agents will converge to the optimal solution.Numerical simulations are presented to illustrate the effectiveness of our proposed method.