Optimal Model Reduction by Time-Domain Moment Matching for Lur'e-Type Models

• 成果类型: Article
• 署名作者: Shakib, Fahim; Scarciotti, Giordano; Jungers, Marc; Pogromsky, Alexander Yu; Pavlov, Alexey; van de Wouw, Nathan
• 署名单位: Imperial College London; Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Eindhoven University of Technology; Norwegian University of Science & Technology (NTNU)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3421809
• 发表日期: 2024
• 页码: 8820-8827
• 关键词: Reduced order systems; Numerical models; Linear systems; CONVERGENCE; Symmetric matrices; steady-state; Time-domain analysis; Bilinear matrix inequalities; coordinate-descent algorithm (CDA); Global stability; Model reduction; moment matching; nonlinear feedback

摘要

This article considers the problem of model reduction for Lur'e-type models consisting of a feedback interconnection between linear dynamics and static nonlinearities. We propose an optimal variant of the time-domain moment-matching method in which the H-infinity -norm of the error transfer-function matrix of the linear part of the model is minimized while the static nonlinearities are inherited from the full-order model. We show that this approach also minimizes an error bound on the L-2 -norm of the steady-state error between the responses of the full-order nonlinear model and the reduced-order nonlinear model. Furthermore, the proposed approach preserves both the Lur'e-type model structure as well as global stability properties. The problem is cast as an optimization problem with bilinear matrix inequality constraints. This problem is then solved using a novel algorithm, although global convergence of the algorithm is not guaranteed. The effectiveness of the approach is illustrated in the reduction of a structural dynamics model of a linear beam with nonlinear supports.