Asymptotically Efficient Quasi-Newton Type Identification with Quantized Observations Under Bounded Persistent Excitations

TL;DR

This paper introduces a novel identification algorithm for dynamical systems with quantized outputs, achieving asymptotic efficiency and optimal convergence rates under bounded persistent excitation conditions.

Contribution

It develops an information-based Quasi-Newton identification algorithm that attains asymptotic efficiency and converges at the optimal rate despite quantized observations.

Findings

The WQNP algorithm converges in mean square and almost surely.

The IBID algorithm asymptotically reaches the Cramer-Rao lower bound.

Numerical examples confirm the effectiveness of the proposed method.

Abstract

This paper is concerned with the optimal identification problem of dynamical systems in which only quantized output observations are available under the assumption of fixed thresholds and bounded persistent excitations. Based on a time-varying projection, a weighted Quasi-Newton type projection (WQNP) algorithm is proposed. With some mild conditions on the weight coefficients, the algorithm is proved to be mean square and almost surely convergent, and the convergence rate can be the reciprocal of the number of observations, which is the same order as the optimal estimate under accurate measurements. Furthermore, inspired by the structure of the Cramer-Rao lower bound, an information-based identification (IBID) algorithm is constructed with adaptive design about weight coefficients of the WQNP algorithm, where the weight coefficients are related to the parameter estimates which leads to the essential difficulty of algorithm analysis. Beyond the convergence properties, this paper demonstrates that the IBID algorithm tends asymptotically to the Cramer-Rao lower bound, and hence is asymptotically efficient. Numerical examples are simulated to show the effectiveness of the information-based identification algorithm.