Journal article
A General Framework for Nonparametric Identification of Nonlinear Stochastic Systems
Wenxiao Zhao, Erik Weyer, George Yin
IEEE Transactions on Automatic Control | Institute of Electrical and Electronics Engineers (IEEE) | Published : 2021
Abstract
In this paper, 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_q,q\geq1 criteria as special cases. First, we prove that the minimizer of the general criterion function converges to the true function value with probability one. Second, recursive algorithms are proposed to find the estim..
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Awarded by Air Force Office of Scientific Research
Funding Acknowledgements
Manuscript received April 14, 2020; accepted July 1, 2020. Date of publication July 7, 2020; date of current version May 27, 2021. The work of Wenxiao Zhao was supported in part by the National Key Research and Development Program of China under Grant 2018YFA0703800 and in part by the National Nature Science Foundation of China under Grant 61822312. The work of Erik Weyer was supported by the Australian Research Council under Grant DP130104028. The work of George Yin was supported in part by the Air Force Office of Scientific Research under Grant FA9550-18-1-0268. Recommended by Associate Editor G. Pillonetto. (Corresponding author: Wenxiao Zhao.)