Adaptive Identification with Guaranteed Performance Under Saturated-Observation and Non-Persistent Excitation

TL;DR

This paper develops a robust adaptive identification method for stochastic systems with saturated observations, providing convergence guarantees and error bounds under minimal excitation conditions, with practical numerical validation.

Contribution

Introduces a two-step Quasi-Newton algorithm for nonlinear stochastic systems with saturation, and proves its convergence and asymptotic normality under weak excitation conditions.

Findings

Global convergence of estimators and predictors established

Asymptotic normality proven under minimal excitation

Probabilistic error bounds derived for finite data

Abstract

This paper investigates the adaptive identification and prediction problems for stochastic dynamical systems with saturated observations, which arise from various fields in engineering and social systems, but up to now still lack comprehensive theoretical studies including performance guarantees needed in practical applications. With this impetus, the paper has made the following main contributions: (i) To introduce a two-step Quasi-Newton (TSQN) algorithm to improve the performance of the identification, which is applicable to a typical class of nonlinear stochastic systems with outputs observed under possibly varying saturation. (ii) To establish the global convergence of both the parameter estimators and adaptive predictors and to prove the asymptotic normality, under the weakest possible non-persistent excitation (PE) condition, which can be applied to stochastic feedback systems with general non-stationary and correlated system signals or data. (iii) To establish useful probabilistic estimation error bounds for any given finite length of data, using either martingale inequalities or Monte Carlo experiments. A numerical example is also provided to illustrate the performance of the proposed identification algorithm.