Efficient convex relaxation for stochastic optimal distributed control problem

Abdulrahman Kalbat, Ramtin Madani, Ghazal Fazelnia, Javad Lavaei

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

15 Citations (Scopus)

Abstract

This paper is concerned with the design of an efficient convex relaxation for the notorious problem of stochastic optimal distributed control (SODC). The objective is to find an optimal structured controller for a dynamical system subject to input disturbance and measurement noise. With no loss of generality, this paper focuses on the design of a static controller for a discrete-time system. First, it is shown that there is a semidefinite programming (SDP) relaxation for this problem with the property that its SDP matrix solution is guaranteed to have rank at most 3. This result is due to the extreme sparsity of the SODC problem. Since this SDP relaxation is computationally expensive, an efficient two-stage algorithm is proposed. A computationally-cheap SDP relaxation is solved in the first stage. The solution is then fed into a second SDP problem to recover a near-global controller with an enforced sparsity pattern. The proposed technique is always exact for the classical H2 optimal control problem (i.e., in the centralized case). The efficacy of our technique is demonstrated on the IEEE 39-bus New England power network, a mass-spring system, and highly-unstable random systems, for which near-optimal stabilizing controllers with global optimality degrees above 90% are designed under a wide range of noise levels.

Original languageEnglish
Title of host publication2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages589-596
Number of pages8
ISBN (Electronic)9781479980093
DOIs
Publication statusPublished - Jan 30 2014
Externally publishedYes
Event2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014 - Monticello, United States
Duration: Sep 30 2014Oct 3 2014

Publication series

Name2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014

Conference

Conference2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014
Country/TerritoryUnited States
CityMonticello
Period9/30/1410/3/14

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications

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