Input Design for Regularized System Identification: Stationary Conditions and Sphere Preserving Algorithm

• 成果类型: Article
• 署名作者: Mu, Biqiang; Kong, He; Chen, Tianshi; Jiang, Bo; Wang, Lei; Wu, Junfeng
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Southern University of Science & Technology; The Chinese University of Hong Kong, Shenzhen; Shenzhen Research Institute of Big Data; The Chinese University of Hong Kong, Shenzhen; Nanjing Normal University; Zhejiang University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3228200
• 发表日期: 2023
• 页码: 5714-5720
• 关键词: Input design; regularized system identification; spherical constraint preserving (SCP) algorithm; stationary points

摘要

This article studies input design of kernel-based regularization methods for linear dynamical systems, which has been formulated as a nonconvex optimization problem with the criterion being a scalar measure of the posterior covariance of the Bayesian estimate, subject to a spherical constraint on the input. The nonconvex nature of such input design problems poses significant challenges in deriving optimality conditions and efficient numerical algorithms. In this work, we first derive a sufficient condition for guaranteeing that a stationary point of the regularized input design problem is a global minimum. Next, we propose a spherical constraint preserving (SCP) algorithm to efficiently reach a stationary point of the design problem. Numerical simulation results show that the SCP algorithm finds the global minimum of the original design problem for all simulated cases and its average computational time is only approximately one tenth of that of the algorithms for previous methods.