Work

Structure-Preserving $H^2$ Optimal Model Reduction Based on the Riemannian Trust-Region Method

Year: 2017

Type: article

Abstract: This paper studies stability- and symmetry-preserving H2optimal model reduction problems of linear systems, which include linear gradient systems as a special case. The problem is formulated as a nonlinear optimization problem on the product manifold of the manifold of symmetric positive-definite matrices and two Euclidean spaces. To solve the problem by using the trust-region method, the gradient and Hessian of the objective function are derived. Furthermore, it is shown that if we restrict our systems to gradient systems, the gradient and Hessian can be obtained more efficiently. More concretely, by symmetry, we can reduce linear matrix equations to be solved. In addition, by a simple example, we show that the solutions to our problem and a similar problem in some literature works are not unique, and the solution sets of both problems do not contain each other in general. Also, it is revealed that the attained optimal values do not coincide. Numerical experiments show that the proposed method gives a reduced system with the same structure with the original system although the balanced truncation method does not.

Source: IEEE Transactions on Automatic Control

DOI: 10.1109/tac.2017.2723259

Authors: Kazuhiro Sato, Hiroyuki Sato

Institutions: Kitami Institute of Technology, Tokyo University of Science

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: Development of Riemannian conjugate gradient methods and their applications to large-scale problems