This paper investigates the distributed online sparse identification problem for the multivariate stochastic regression models over sensor networks, enabling all sensors to cooperatively estimate the unknown multi-dimensional sparse parameter matrix by using local information from neighbors. Existing distributed sparse estimation methods, including & ell;1 regularization, often rely on offline optimization/batch processing, or impose restrictive independence assumptions on the regressors. To overcome these challenges, we first introduce an auxiliary variable matrix into each sensor's cost function, constructing a bivariate local criterion function. Building on this, we propose a novel distributed online sparse identification algorithm by integrating alternating minimization with adaptive thresholding techniques, which can effectively resolve the non-differentiability issue inherent of & ell;1 regularization in online settings. Theoretically, under the weakest possible cooperative non-persistent excitation condition, we rigorously establish the almost sure convergence of parameter estimates and precisely characterize their convergence rate. Furthermore, we prove that the proposed algorithm guarantees finite-time exact recovery of the support set in the unknown parameter matrix through an adaptive weighting mechanism. Notably, our analysis removes restrictive independence assumptions on regression vectors, making it suitable for closed-loop stochastic feedback systems. Finally, the numerical examples are provided to demonstrate the effectiveness and superiority of our theoretical results. (c) 2026 Published by Elsevier Ltd.

Publication:

AUTOMATICA

http://dx.doi.org/10.1016/j.automatica.2026.113167

Author:

Die Gan

School of Mathematical Sciences, Fudan University, Shanghai 200433, China

The State Key Laboratory of Autonomous Intelligent Unmanned Systems, Beijing, China

E-mail addresses: gandie@amss.ac.cn

Zhixin Liu

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

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

Corresponding author

E-mail addresses: lzx@amss.ac.cn