Kernel Regression-Based State-Space Estimation of Continuous-Time Dynamic Systems From Noisy Sampled State Data

• 成果类型: Article
• 署名作者: Kim, Taekyoo
• 署名单位: Korea Railroad Research Institute (KRRI)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3354191
• 发表日期: 2024
• 页码: 4757-4764
• 关键词: Kernel; Noise measurement; estimation; System identification; research and development; quadratic programming; optimization; Block coordinate descent; kernel regression; reproducing kernel Hilbert spaces (RKHS); state-space identification

摘要

Despite various physical applications, state-space identification for continuous-time dynamic systems with noisy sampled data is less popular than discrete-time systems owing to unmeasurable state derivatives. Consequently, its scope is limited to linear or preparameterized systems. In this study, we formulate the identification as a (nonparametric) kernel regression problem applicable to nonlinear dynamic systems, which facilitates the joint assessment of the data fitness and fidelity of dynamics, that is, the error between the state derivative and the vector field. This is realized by employing smooth kernels, which facilitate the embedding of the state derivative into the reproducing kernel Hilbert space. To demonstrate the feasibility of the formulation, we extend the representer theorem, resulting in a finite dimensional albeit nonconvex minimization problem. To achieve fast linear estimation despite the nonconvexity, we propose a practical algorithm, called state-dynamics alternate descent, which is basically an unconstrained iterated quadratic programming. Furthermore, the proposed method was evaluated using the example of a simple nonlinear pendulum.