Distributed multi-agent optimization subject to nonidentical constraints and communication delays

In this paper, we study a distributed optimization problem using a subgradient projection algorithm for multi-agent systems subject to nonidentical constraints and communication delays under local communication. Here the agents capable of communicating with their local neighbors are constrained to r...

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Published in:Automatica (Oxford) Vol. 65; pp. 120 - 131
Main Authors: Lin, Peng, Ren, Wei, Song, Yongduan
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.03.2016
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ISSN:0005-1098, 1873-2836
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Abstract In this paper, we study a distributed optimization problem using a subgradient projection algorithm for multi-agent systems subject to nonidentical constraints and communication delays under local communication. Here the agents capable of communicating with their local neighbors are constrained to remain in possibly different closed convex sets and optimize a global objective function composed of a sum of local objective functions, each of which is known to only one agent. First, we consider the case of fixed graphs and show that distributed optimization might not be achieved on general strongly connected directed graphs. Instead, the agents optimize a weighted sum of the local objective functions. Then we consider the case of switching graphs and show that distributed optimization can be achieved when the adjacency matrices are doubly stochastic and the union of the directed graphs is strongly connected among each time interval of a certain bounded length. Furthermore, we consider the case of communication delays, where the delays are mutually independent. It is shown that the distributed optimization problem can be solved by introducing additional delays to the subgradient projection algorithm and the communication delays can be arbitrarily bounded. Finally, numerical examples are included to show the obtained theoretical results.
AbstractList In this paper, we study a distributed optimization problem using a subgradient projection algorithm for multi-agent systems subject to nonidentical constraints and communication delays under local communication. Here the agents capable of communicating with their local neighbors are constrained to remain in possibly different closed convex sets and optimize a global objective function composed of a sum of local objective functions, each of which is known to only one agent. First, we consider the case of fixed graphs and show that distributed optimization might not be achieved on general strongly connected directed graphs. Instead, the agents optimize a weighted sum of the local objective functions. Then we consider the case of switching graphs and show that distributed optimization can be achieved when the adjacency matrices are doubly stochastic and the union of the directed graphs is strongly connected among each time interval of a certain bounded length. Furthermore, we consider the case of communication delays, where the delays are mutually independent. It is shown that the distributed optimization problem can be solved by introducing additional delays to the subgradient projection algorithm and the communication delays can be arbitrarily bounded. Finally, numerical examples are included to show the obtained theoretical results.
Author Lin, Peng
Song, Yongduan
Ren, Wei
Author_xml – sequence: 1
  givenname: Peng
  surname: Lin
  fullname: Lin, Peng
  email: lin_peng0103@sohu.com
  organization: School of Electronic and Information Engineering, Xi’an Jiaotong University, China
– sequence: 2
  givenname: Wei
  surname: Ren
  fullname: Ren, Wei
  email: ren@ee.ucr.edu
  organization: Department of Electrical and Computer Engineering, University of California, Riverside, USA
– sequence: 3
  givenname: Yongduan
  surname: Song
  fullname: Song, Yongduan
  email: ydsong@cqu.edu.cn
  organization: Key Laboratory of Dependable Service Computing, Cyber Physical Society of Ministry of Education, Chongqing University, China
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Keywords Distributed optimization
Switching topologies
Cooperative control
Communication delays
Multi-agent systems
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Snippet In this paper, we study a distributed optimization problem using a subgradient projection algorithm for multi-agent systems subject to nonidentical constraints...
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SubjectTerms Algorithms
Communication delays
Cooperative control
Delay
Distributed optimization
Graph theory
Graphs
Mathematical analysis
Mathematical models
Multi-agent systems
Optimization
Projection
Switching topologies
Title Distributed multi-agent optimization subject to nonidentical constraints and communication delays
URI https://dx.doi.org/10.1016/j.automatica.2015.11.014
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Volume 65
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