2023/02/16 by Xiaodong Cheng, Cheng, Xiaodong · 2 citations
Computer Science · Physics and Astronomy · #FOS: Mathematics #Model Reduction and Neural Networks #Neural Networks and Applications #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2302.08627
openalex publication_date 2023/02/16 · openalex created_date 2023/02/21 · openalex updated_date 2026/07/28
This paper presents a structure-preserving model reduction framework for linear systems, in which the H2 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 H2 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.