A Jacobi decomposition algorithm for distributed convex optimization in Distributed Model Predictive Control

Minh Dang Doan, Moritz Diehl, Tamas Keviczky, Bart De Schutter

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

4 Citations (Scopus)
47 Downloads (Pure)

Abstract

In this paper we introduce an iterative distributed Jacobi algorithm for solving convex optimization problems, which is motivated by distributed model predictive control (MPC) for linear time-invariant systems. Starting from a given feasible initial guess, the algorithm iteratively improves the value of the cost function with guaranteed feasible solutions at every iteration step, and is thus suitable for MPC applications in which hard constraints are important. The proposed iterative approach involves solving local optimization problems consisting of only few subsystems, depending on the flexible choice of decomposition and the sparsity structure of the couplings. This makes our approach more applicable to situations where the number of subsystems is large, the coupling is sparse, and local communication is available. We also provide a method for checking a posteriori centralized optimality of the converging solution, using comparison between Lagrange multipliers of the local problems. Furthermore, a theoretical result on convergence to optimality for a particular distributed setting is also provided.

Original languageEnglish
Title of host publicationIFAC-PapersOnLine
Subtitle of host publicationProceedings 20th IFAC World Congress
EditorsDenis Dochain, Didier Henrion, Dimitri Peaucelle
Place of PublicationLaxenburg, Austria
PublisherElsevier
Pages4905-4911
Volume50-1
DOIs
Publication statusPublished - 2017
Event20th World Congress of the International Federation of Automatic Control (IFAC), 2017 - Toulouse, France
Duration: 9 Jul 201714 Jul 2017
Conference number: 20
https://www.ifac2017.org

Publication series

NameIFAC-PapersOnLine
Number1
Volume50

Conference

Conference20th World Congress of the International Federation of Automatic Control (IFAC), 2017
Abbreviated titleIFAC 2017
CountryFrance
CityToulouse
Period9/07/1714/07/17
Internet address

Keywords

  • cooperative optimization algorithm
  • distributed model predictive control
  • distributed optimization
  • Jacobi algorithm

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