Optimal state feedback controllers with strict row sparsity constraints

Reza Arastoo, Yaser Ghaedsharaf, Mayuresh V. Kothare, Nader Motee

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

Abstract

This paper considers the problem of optimal row sparse state feedback controller design for LTI systems, where the controller is assumed to be static with pre-specified structural constraint. Incongruous to the existing literature on the sparsity promoting control synthesis, we do not employ convex relaxation of the sparsity representing terms, such as ℓ0-norm of the controller gain, in our proposed framework. Borrowing the results from the theory of majorization, we develop an exact rank constrained reformulation of the s-sparse vector recovery from a convex set, and, then, utilized it to cast our row sparse control problem into a an optimization problem where all constraints are convex, except a single rank constraint. Furthermore, we propose a necessary and sufficient condition for the feasibility of a stabilizing row s-sparse controller, and exploited it to propose a bi-linear minimization problem, subject to convex constraints, which solve the derived equivalent rank constrained problem to deliver an optimal row sparse state feedback controller. The benefits of approach are demonstrated though several numerical simulations.

Original languageEnglish (US)
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1948-1953
Number of pages6
Volume2016-July
ISBN (Electronic)9781467386821
DOIs
StatePublished - Jul 28 2016
Externally publishedYes
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Other

Other2016 American Control Conference, ACC 2016
Country/TerritoryUnited States
CityBoston
Period7/6/167/8/16

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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