Sparse System Identification for Stochastic Feedback Control Systems

TL;DR

This paper presents a novel sparse parameter identification method for stochastic feedback control systems, ensuring accurate zero/nonzero element recovery and convergence, applicable to various control and identification tasks.

Contribution

It introduces an L2 norm with L1 regularization algorithm with adaptive weights for sparse system identification under feedback control, with proven set and parameter convergence.

Findings

Correctly identifies zero and nonzero parameters with probability one.

Estimates of nonzero parameters converge almost surely to true values.

Applicable to variable selection, open-loop, and closed-loop stochastic system identification.

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.