Focusing on identification, this article develops a class of convex optimization-based criteria and correspondingly the recursive algorithms to estimate the parameter vector theta* of a stochastic dynamic system. Not only do the criteria include the classical least-squares estimator but also the L-l = |center dot |(l), l >= 1, the Huber, the Log-cosh, and the Quantile costs as special cases. First, we prove that the minimizers of the convex optimization-based criteria converge to theta* with probability one. Second, the recursive algorithms are proposed to find the estimates, which minimize the convex optimization-based criteria, and it is shown that these estimates also converge to the true parameter vector with probability one. Numerical examples are given, justifying the performance of the proposed algorithms including the strong consistency of the estimates, the robustness against outliers in the observations, and high efficiency in online computation due to the recursive nature.

Publication:

IEEE TRANSACTIONS ON AUTOMATIC CONTROL

http://dx.doi.org/10.1109/TAC.2025.3628997

Author:

Mingxia Ding

the State Key Laboratory of Mathematical Sciences (SKLMS), Academy Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

the School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

e-mail: dingmingxia@ amss.ac.cn

Wenxiao Zhao

the State Key Laboratory of Mathematical Sciences (SKLMS), Academy Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

the School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: Wenxiao Zhao

e-mail: wxzhao@amss.ac.cn

Tianshi Chen

the School of Data Science and Engineering and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen 518172, China

e-mail: tschen@cuhk.edu.cn

Weidong Zhang

the School of Information and Communication Engineering, Hainan University, Haikou 570228, China, and also with the Department of Automation, Shanghai Jiaotong University, Shanghai 200240, China

e-mail: wdzhang@sjtu.edu.cn