Application of a Message-Passing Decomposition of Sparsely-Coupled Linear Programming Problems to the Uniform Stabilization of Positive Switched Linear Systems

Ray Essick, Geir Dullerud

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We apply a distributed, message-passing scheme for sparsely-coupled linear programming problems to the stabilization of positive switched linear systems. We first develop exact conditions for the existence of a stabilizing path-dependent controller for positive switched linear systems in terms of an increasing family of linear programming (LP) problems. These results are of independent interest as a special case of the stabilization of arbitrary switched linear systems. The size of each member of this family of LPs grows combinatorially in both the number of switching modes and the path-length of the controller. We then make use of a problem decomposition for sparsely-coupled linear programming problems by decomposing the induced switching graph for the system. The resulting problem decomposition can be solved in parallel using distributed computing resources. An example problem and its decomposition are presented to facilitate discussion of this approach and to highlight future areas of interest for our particular problem formation.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3780-3785
Number of pages6
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Publication series

NameProceedings of the American Control Conference
Volume2018-June
ISSN (Print)0743-1619

Other

Other2018 Annual American Control Conference, ACC 2018
CountryUnited States
CityMilwauke
Period6/27/186/29/18

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ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Essick, R., & Dullerud, G. (2018). Application of a Message-Passing Decomposition of Sparsely-Coupled Linear Programming Problems to the Uniform Stabilization of Positive Switched Linear Systems. In 2018 Annual American Control Conference, ACC 2018 (pp. 3780-3785). [8431432] (Proceedings of the American Control Conference; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431432