It is well known that saturated output observations are prevalent in various practical systems and that the & ell;(1)-norm is more robust than the & ell;(2)-norm-based parameter estimation. Unfortunately, adaptive identification based on both saturated observations and the & ell;(1)-optimization turns out to be a challenging nonlinear problem, and has rarely been explored in the literature. Motivated by this and the need to fit with the & ell;(1)-based index of prediction accuracy in, e.g., judicial sentencing prediction problems, we propose a two-step weighted & ell;(1)-based adaptive identification algorithm. Under certain excitation conditions much weaker than the traditional persistent excitation condition, we will establish the global convergence of both the parameter estimators and the adaptive predictors. It is worth noting that our results do not rely on the widely used independent and identically distributed assumptions on the system signals, and thus, do not exclude applications to feedback control systems. We will demonstrate the advantages of our proposed new adaptive algorithm over the existing & ell;(2)-based ones, through both a numerical example and a real-data-based sentencing prediction problem.

Publication:

IEEE TRANSACTIONS ON AUTOMATIC CONTROL

http://dx.doi.org/10.1109/TAC.2025.3547950

Author:

Lei Guo (Corresponding author)

the State Key Laboratory of MathematicalSciences, Academy of Mathematics and Systems Science, ChineseAcademy of Sciences, Beijing 100190, China

theSchool of Mathematical Science, University of Chinese Academy of

Sciences, Beijing 100049, China

e-mail: lguo@amss.ac.cn

Xin Zheng

the State Key Laboratory of MathematicalSciences, Academy of Mathematics and Systems Science, ChineseAcademy of Sciences, Beijing 100190, China

theSchool of Mathematical Science, University of Chinese Academy of

Sciences, Beijing 100049, China

e-mail: zhengxin2021@amss.ac.cn