DocumentCode :
37962
Title :
Dissipativity-Preserving Model Reduction for Large-Scale Distributed Control Systems
Author :
Ishizaki, Takayuki ; Sandberg, Henrik ; Kashima, Kenji ; Imura, Jun-ichi ; Aihara, Kazuyuki
Author_Institution :
Grad. Sch. of Inf. Sci. & Eng., Tokyo Inst. of Technol., Tokyo, Japan
Volume :
60
Issue :
4
fYear :
2015
fDate :
Apr-15
Firstpage :
1023
Lastpage :
1037
Abstract :
We propose a dissipativity-preserving structured model reduction method for distributed control systems. As a fundamental tool to develop structured model reduction, we first establish dissipativity-preserving model reduction for general linear systems on the basis of a singular perturbation approximation. To this end, by deriving a tractable expression of singular perturbation models, we characterize dissipativity preservation in terms of a projection-like transformation of storage functions, and we show that the resultant approximation error is relevant to the sum of neglected eigenvalues of an index matrix. Next, utilizing this dissipativity-preserving model reduction, we develop a structured controller reduction method for distributed control systems. The major significance of this method is to preserve the spatial distribution of dissipative controllers and to provide an a priori bound for the performance degradation of closed-loop systems in terms of the H2-norm. The efficiency of the proposed method is verified through a numerical example of vibration suppression control for interconnected second-order systems.
Keywords :
H control; approximation theory; closed loop systems; distributed control; eigenvalues and eigenfunctions; large-scale systems; matrix algebra; reduced order systems; singularly perturbed systems; H2-norm; a-priori bound; approximation error; closed-loop systems; dissipative controllers; dissipativity-preserving structured model reduction method; eigenvalues; general linear systems; index matrix; interconnected second-order systems; large-scale distributed control systems; performance degradation; projection-like transformation; singular perturbation approximation; spatial distribution; storage functions; structured controller reduction method; tractable expression; vibration suppression control; Approximation methods; Decentralized control; Graphical models; Linear systems; Periodic structures; Reduced order systems; Dissipativity Preservation; Dissipativity preservation; Distributed Control Systems; Singular Perturbation Approximation; Structured Model Reduction; distributed control systems; singular perturbation approximation; structured model reduction;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.2014.2370271
Filename :
6954451
Link To Document :
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