Distributed Optimization of Multiagent Systems in Directed Networks with Time-Varying Delay

Junxiu Yan,Hui Yu

doi:10.1155/2017/7937916

Abstract

This paper addresses a distributed consensus optimization problem of a first-order multiagent system with time-varying delay. A continuous-time distributed optimization algorithm is proposed. Different from most ways of solving distributed optimization problem, the Lyapunov-Razumikhin theorem is applied to the convergence analysis instead of the Lyapunov-Krasovskii functionals with LMI conditions. A sufficient condition for the control parameters is obtained to make all the agents converge to the optimal solution of the system. Finally, an example is given to validate the effectiveness of our theoretical result.

Highlights

The distributed optimization problem of multiagent systems has been investigated by many researchers; researches on distributed optimization and control theorem have been developing rapidly and have been applied to various fields of industry and defense, like smart grid [1, 2], sensor networks [3], social networks [4], and so on
In both papers [9, 11], discretetime subgradient algorithms are proposed for unconstrained, separable, convex optimization problem and each agent communicates with the other agents over a time-varying network topology
A projected consensus subgradient algorithm is proposed for constrained optimization problem in [10], and, in [12], the authors devise two distributed primaldual subgradient algorithms over networks with dynamically changing topologies but satisfying a standard connectivity property

Summary

Introduction

The distributed optimization problem of multiagent systems has been investigated by many researchers; researches on distributed optimization and control theorem have been developing rapidly and have been applied to various fields of industry and defense, like smart grid [1, 2], sensor networks [3], social networks [4], and so on. The current literatures about distributed optimization problems are more focused on discrete-time algorithms (see [9,10,11,12] and references therein) In both papers [9, 11], discretetime subgradient algorithms are proposed for unconstrained, separable, convex optimization problem and each agent communicates with the other agents over a time-varying network topology. From the control system viewpoint, a continuous-time multiagent system dynamic is proposed with undirected communication topology [13]; the algorithm is further investigated over a strongly connected and weight balanced directed graph [16], and even a modified system is proposed in [14] with auxiliary-variables no longer needing to exchange information. In order to avoid using auxiliary-variables, a family of ZeroGradient-Sum algorithms are proposed over fixed communication topology in [19]

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Conclusion