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Model Reduction Problem (model + reduction_problem)

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Selected Abstracts

A remark on ,Model reduction for singular systems via covariance approximation'

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2006
Dabo Xu
Abstract This note comments on the results of the paper, ,Model reduction for singular systems via covariance approximation', (Optim. Contr. Appl. Meth. 2004; 25:263,278), which studied model reduction for singular system via covariance approximation. Although the proposed new error criterion reflects the capacity of the impulsive behaviour for singular systems, there exists shortcomings due to the fixed matrix Br in the process of optimization, which remarkably matters. In order to avoid this drawback, the model reduction problem is reformulated and a genetic algorithm is used to deal with the optimization problem. A numerical example is provided to show the effectiveness and improvement of the proposed algorithm. Copyright © 2006 John Wiley & Sons, Ltd. [source]

On ,, model reduction for discrete-time linear time-invariant systems using linear matrix inequalities,

ASIAN JOURNAL OF CONTROL, Issue 3 2008
Yoshio Ebihara
Abstract In this paper, we address the ,, model reduction problem for linear time-invariant discrete-time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well-known lower bounds on the approximation error, which is given in terms of the Hankel singular values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the ,, optimal reduced-order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting. [source]

Computationally Efficient Algorithm For Frequency-Weighted Optimal H, Model Reduction

ASIAN JOURNAL OF CONTROL, Issue 3 2003
Fen Wu
ABSTRACT In this paper, a frequency-weighted optimal H, model reduction problem for linear time-invariant (LTI) systems is considered. The objective of this class of model reduction problems is to minimize H, norm of the frequency-weighted truncation error between a given LTI system and its lower order approximation. A necessary and sufficient solvability condition is derived in terms of LMIs with one extra coupling rank constraint, which generally leads to a non-convex feasibility problem. Moreover, it has been shown that the reduced-order model is stable when both stable input and output weights are included, and its state-space data are given explicitly by the solution of the feasibility problem. An efficient model reduction scheme based on cone complementarity algorithm (CCA) is proposed to solve the non-convex conditions involving rank constraint. [source]