Distributed Optimization Of Multiagent Systems With Guaranteed Convergence Rate Performance

Large-scale networked systems have complex dynamic characteristics,making it important and challenging to optimization problem.Compared with the traditional centralized optimization,distributed optimization has the following advantages: such as easy to extend,high flexibility,strong cooperation and less privacy data leakage.Therefore,it has wide application in large-scale machine learning,economic dispatch of smart grid,optimal resource allocation of sensor networks,multi-robot system positioning and so on.With the rapid development of multi-agent cooperative technique,distributed optimization has been widely concerned in recent years.In particular,because some practical optimization problems have high requirements for convergence rate(such as economic dispatch problem of microgrid),it is of great importance and significance to study the distributed optimization algorithm with guaranteed convergence rate performance.Based on convex optimization theory,algebraic graph theory and distributed cooperative control,this paper studies the distibuted optimization problem with guaranteed convergence rate under the framework of network multi-agent system.The main contribution of this work are as follows:(1)For a class of second-order nonlinear multi-agent systems,the distributed optimization control problem,which aims to satisfy a constrained global optimal objective,is formulated in this paper.In the weight-balanced graph,based on the defined auxiliary variables,gradient function and proportional integral protocol,a distributed optimal control algorithm with exponential convergence rate is designed.Furthermore,with the help of Lyapunov functions,it is proved that the algorithm has fast exponential convergence and the specific exponential convergence rate is estimated.By embedding the estimator of left eigenvector of the Laplacian matrix,the proposed method is further extended to the case of unbalanced communication topology.This work provides a solution for the optimal control problem with exponential convergence under directed topology.(2)In this paper,the exponential convergence of non-strongly convex objective function is investigated.For a class of non-strongly convex global optimization of multi-agent network with equality and set constraints,we study its exponential convergence under continuous-time communication and event-triggered communication.At present,much efforts have been given to prove the exponential convergence of sophisticated distibuted designs for strongly convex assumption.In order to relax this assumption,we first introduce the metric subregularity condtion.By using this condition,the adding integrator technology,gradient descent method,projection operator and auxiliary variables,a distributed optimization algorithm with exponential convergence rate for non-strongly convex objective function is proposed.In order to reduce the communication cost among agents,we further introduce the event-triggering mechanism.The distributed event-triggered optimization protocol can not only guarantee the exponential convergence under the condition of non-strongly convex objective function,but also reduce the network communication cost and the computational burden of agents.(3)For a class of global optimization of multi-agent network with equality and inequality constraints,a novel distributed fixed-time convergence algorithm is designed by combining fraction order technique,symbolic function and projection operator.The rigorous convergence analysis is given by constructing novel Lyapunov functions.However,the settling time is related to the design parameters of the distributed optimization algorithm.In order to furhter design a predefined-time protocol,where the settling time can be set by the user in advance,we design a novel predefined-time distributed optimization algorithm by time based generator(TBG)technique and penalty function method.It is shown that the decision variables converge to the neighborhood of the optimal solution in a pre-given time and the neighborhood is adjustable.(4)For a class of global optimization of multi-agent network with equality and set constraints,by using TBG technology,dynamic event-triggered mechanism,projection operator,tangent cone technique and Laypunov theory,we design a novel distributed optimization algorithm,which can not only guarantee the converence rate but also reduce the communication burdens.Thus,it solves the problem that the existing mthods can not simultaneously achieve the predefined-time optimization and reduce the communication burdens.