DocumentCode :
1301191
Title :
Performance Optimization of Switched Systems: A Model Matching Approach
Author :
Jiang, Shengxiang ; Voulgaris, Petros G.
Author_Institution :
Mech. Sci. & Eng. Dept., Univ. of Illinois, Urbana, IL, USA
Volume :
54
Issue :
9
fYear :
2009
Firstpage :
2058
Lastpage :
2071
Abstract :
In this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n stable linear time-invariant (LTI) systems. The interest is placed on optimizing the worst-case performance of this model matching system over all possible switchings with either l infin-induced norm or H 2 norm as the performance criterion. This optimization is performed over all Youla-Kucera parameters that switch causally in time among n stable LTI systems. For the particular setup at hand, it is shown that the optimal Youla-Kucera parameter need not depend on the switching trajectory in the cases of partially matched switching and unmatched switching, and that it can be obtained as an LTI solution to an associated standard l 1 or H 2 optimization. In the case of matched switching, two convergent sequences to the optimal solution from above and below are formulated in terms of linear programs and quadratic programs respectively for the l infin-induced and H 2 norm optimizations. An approximate solution with any given precision is possible by finite truncation. Applications of these results to sensitivity minimization, linear switched parameter systems, and cooperative control are provided.
Keywords :
control system synthesis; convergence; cooperative systems; linear programming; linear systems; minimisation; quadratic programming; stability; H2 optimization; Youla-Kucera parameters; convergent sequences; cooperative control; finite truncation; linear programs; linear switched parameter systems; linear time-invariant systems; model matching approach; partially matched switching; performance optimization; prototypical model matching problem; quadratic programs; sensitivity minimization; stable LTI systems; switched systems; switching trajectory; unmatched switching; worst-case performance; Books; Control system synthesis; Control systems; Optimization; Prototypes; Signal analysis; Signal mapping; Signal synthesis; Switched systems; Switches; ${cal H}_{2}$ optimal; $ell_{1}$ optimization; $ell_{infty}$-induced; Arbitrary switching; Youla–Kucera parameter; cooperative control;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.2009.2026928
Filename :
5208242
Link To Document :
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