This article studies the control-oriented recursive identification of finite impulse response systems with binary-valued observations. Inspired by the maximum likelihood method, a novel recursive algorithm is proposed using the statistical property of system noises and observations. Unlike existing research, the gradient of the proposed algorithm is derived from the local likelihood function, which has not been previously considered. The core advantage of the algorithm is the adaptation of the recursive weight term, and especially, it has an accelerating effect when the estimated value deviates far from the true value. Besides, compared with existing algorithm based on time-varying thresholds, the proposed algorithm makes it applicable to fixed threshold scenarios through weighting, thus avoiding the complexity caused by time-varying thresholds. The proposed algorithm is proved to be convergent in both almost sure and mean square sense. Furthermore, the almost sure and mean square convergence rates are also obtained under some mild conditions. Two simulations are presented to demonstrate the effectiveness of the proposed algorithm and the advantage of the convergence rate over existing algorithm.

Publication:

IEEE TRANSACTIONS ON AUTOMATIC CONTROL

http://dx.doi.org/10.1109/TAC.2025.3649296

Author:

Li, Xin

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Email address: lixin2020@amss.ac.cn

Shao, Mingjie

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Univ Chinese Acad Sci, Sch Math Sci, Beijing 100149, Peoples R China

Email address: mingjieshao@amss.ac.cn

Zhang, Ji-Feng

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Zhongyuan Univ Technol, Sch Automat & Elect Engn, Zhengzhou 450007, Peoples R China

Email address: jif@iss.ac.cn

Zhao, Yanlong(corresponding author)

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Univ Chinese Acad Sci, Sch Math Sci, Beijing 100149, Peoples R China

Email address:ylzhao@amss.ac.cn