Sparse System Identification for Stochastic Feedback Control Systems

Wenxiao Zhao; George G Yin; Er-Wei Bai

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Sparse System Identification for Stochastic Feedback Control Systems

Wenxiao Zhao, George G Yin and Er-Wei Bai

ArXiv.org

09/03/2019

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https://arxiv.org/abs/1909.00972View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Focusing on identification, this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector of a stochastic dynamic system under feedback control, for which the current input may depend on the past inputs and outputs, system noises as well as exogenous dithers. First, a sparse parameter identification algorithm is introduced based on L2 norm with L1 regularization, where the adaptive weights are adopted in the optimization variables of L1 term. Second, estimates generated by the algorithm are shown to have both set and parameter convergence. That is, sets of the zero and nonzero elements in the parameter can be correctly identified with probability one using a finite number of observations, and estimates of the nonzero elements converge to the true values almost surely. Third, it is shown that the results are applicable to a large number of applications, including variable selection, open-loop identification, and closed-loop control of stochastic systems. Finally, numerical examples are given to support the theoretical analysis.

Details

Title: Subtitle: Sparse System Identification for Stochastic Feedback Control Systems
Creators: Wenxiao Zhao
George G Yin
Er-Wei Bai
Resource Type: Preprint
Publication Details: ArXiv.org
ISSN: 2331-8422
Language: English
Date posted: 09/03/2019
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984197912502771

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