Distributed Optimization on Unbalanced Time-Varying Topologies: Theories and Experiments

Zhenhong Li, Tianqiao Zhao, Zhengtao Ding

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper considers distributed optimization problems on both fixed and time-varying directed communication structures within a continuous-time framework. Different from most existing results in literature on continuous-time optimization, the lower bound of local convexity constants are unknown, and the requirement of weight-balanced communication structures is removed. An augmented Lagrangian function is designed to analyze the properties of optimal solutions over an asymmetric Laplacian matrix. Based on this analysis, a consensus-based algorithm is proposed to solve the distributed optimization problem on unbalanced directed graphs such that the algorithm asymptotically converges to optimal solutions. Furthermore, an algorithm is proposed to solve the distributed optimization problem on unbalanced time-varying communication topologies. A novel Lyapunov function including a semi-positive definite term is designed to establish the convergence analysis of this algorithm. By exploring certain features of positive invariance sets and asymmetric Laplacian matrices, sufficient conditions for the convergence are established. Two experiments are carried out on a distributed microcomputer platform, thus validating the proposed algorithms.

Original languageEnglish
Title of host publicationProceedings of the 37th Chinese Control Conference, CCC 2018
EditorsXin Chen, Qianchuan Zhao
PublisherIEEE Computer Society
Pages6878-6883
Number of pages6
ISBN (Electronic)9789881563941
DOIs
Publication statusPublished - 5 Oct 2018
Event37th Chinese Control Conference, CCC 2018 - Wuhan, China
Duration: 25 Jul 201827 Jul 2018

Publication series

NameChinese Control Conference, CCC
Volume2018-July
ISSN (Print)1934-1768
ISSN (Electronic)2161-2927

Conference

Conference37th Chinese Control Conference, CCC 2018
Country/TerritoryChina
CityWuhan
Period25/07/1827/07/18

Keywords

  • Consensus control
  • Distributed optimization
  • Time-varying topologies
  • Unbalanced graph

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