A General Framework for Nonparametric Identification of Nonlinear Stochastic Systems

• 成果类型: Article
• 署名作者: Zhao, Wenxiao; Weyer, Erik; Yin, George
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; University of Melbourne; Wayne State University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3007569
• 发表日期: 2021
• 页码: 2449-2464
• 关键词: Convex optimization; nonlinear autoregressive systems with exogenous inputs (NARX); Nonparametric; identification; stochastic approximation; strong consistency

摘要

In this article, nonparametric identification of nonlinear autoregressive systems with exogenous inputs (NARX) is considered; a general criterion function is introduced for estimating the value of the nonlinear function within the system at any fixed point. The criterion function is constructed using a kernel together with a convex objective function. Not only does this framework include the classical kernel-based weighted least-squares estimator but also the kernel-based L-l, l >= 1 criteria as special cases. First, we prove that the minimizer of the general criterion function converges to the true function value with probability 1. Second, recursive algorithms are proposed to find the estimates, which minimize the criterion function, and it is shown that these estimates also converge to the true function value with probability 1. Numerical examples are given, justifying that the framework guarantees the strong consistency of the estimates and exhibits the robustness against outliers in the observations.