Distributed Optimization Algorithm for Discrete-Time Heterogeneous Multi-Agent Systems With Nonuniform Stepsizes

Lipo Mo,Jingyi Li,Jian Huang

doi:10.1109/access.2019.2925414

Abstract

This paper is devoted to the distributed optimization problem of heterogeneous multi-agent systems, where the communication topology is jointly strongly connected and the dynamics of each agent is the first-order or second-order integrator. A new distributed algorithm is first designed for each agent based on the local objective function and the local neighbors’ information that each agent can access. By a model transformation, the original closed-loop system is converted into a time-varying system and the system matrix of which is a stochastic matrix at any time. Then, by the properties of the stochastic matrix, it is proven that all agents’ position states can converge to the optimal solution of a team objective function provided the union communication topology is strongly connected. Finally, the simulation results are provided to verify the effectiveness of the distributed algorithm proposed in this paper.

Highlights

Distributed control theory has gained the fast progress due to the traditional centralized control methods, such as [1], [2], have been unable to meet the demands of control engineering
We mainly study the distributed optimization problem of heterogeneous multi-agent system with jointly strongly connected communication topologies
(2) In contrast to [25], [32], [35], [37], where the distributed optimization problems were studied for first-order or secondorder multi-agent systems, this paper extends these results to heterogeneous multi-agent systems including first-order and second-order integrators simultaneously, which brings us more challenges and difficulties due to the inconsistency of each agent’s dynamics

Summary

Introduction

Distributed control theory has gained the fast progress due to the traditional centralized control methods, such as [1], [2], have been unable to meet the demands of control engineering. Convex and nonconvex constrained consensus problems were considered for discrete-time and continuoustime multi-agent systems in [7]–[9], some effective distributed algorithms were designed and some consensus conditions were obtained. For firstorder multi-agent systems, the subgradient method was introduced to optimize a sum of convex functions [21], [22]. These results were extended to continuous-time situations [23]–[25]. Taken the identical or nonidentical constraint sets into account, the distributed optimization problems were solved by a subgradient projection algorithm for general convex objective

Objectives

Results

Conclusion