An Optimal Projection Framework for Structure-Preserving Model Reduction of Linear Systems

Xiaodong Cheng

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arXiv · 2302.08627

An Optimal Projection Framework for Structure-Preserving Model Reduction of Linear Systems

Xiaodong Cheng

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Abstract

This paper presents a structure-preserving model reduction framework for linear systems, in which the $\mathcal{H}_2$ optimization is incorporated with the Petrov-Galerkin projection to preserve structural features of interest, including dissipativity, passivity, and bounded realness. The model reduction problem is formulated in a nonconvex optimization setting on a noncompact Stiefel manifold, aiming to minimize the $\mathcal{H}_2$ norm of the approximation error between the full-order and reduced-order models. The explicit expression for the gradient of the objective function is derived, and two gradient descent procedures are applied to seek for a (local) minimum, followed by a theoretical analysis on the convergence properties of the algorithms. Finally, the performance of the proposed method is demonstrated by two numerical examples which consider stability-preserving and passivity-preserving model reduction problems, respectively.

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Xiaodong Cheng. 2023-02-16. An Optimal Projection Framework for Structure-Preserving Model Reduction of Linear Systems. https://arxiv.org/abs/2302.08627

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