On ℓ performance optimization of switched systems

Shengxiang Jiang, Petros G. Voulgaris

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

Abstract

In this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n given linear time invariant (LTI) systems. The interest is placed on minimizing the worst case ℓ -induced norm of this model matching system over all possible switchings. This minimization is performed over all Youla-Kucera parameters Q that switch causally in time over n (stable) LTI systems. For the particular set-up at hand, it is shown that the optimal Youla-Kucera parameter Q need not depend on the switching sequence in the case of partially matched switching, and that it can be obtained as an LTI solution to an associated standard ℓ1 optimization. In the case of matched switching, two convergent sequences to the optimal solution from above and below respectively are formulated in linear programming, and an approximate solution with any given precision is possible by finite truncation.

Original languageEnglish (US)
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages5011-5016
Number of pages6
DOIs
StatePublished - Dec 1 2007
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other46th IEEE Conference on Decision and Control 2007, CDC
CountryUnited States
CityNew Orleans, LA
Period12/12/0712/14/07

Keywords

  • Worst case switching
  • ℓ optimal
  • ℓ-induced optimality

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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