Convergence Analysis of a Robust Recursive Identification Method for Autoregressive Models

Abstract

Recently the concept of robustness has attracted considerable attention of control engineers for several control problems. One of this direction is robust identification. Polyak and Tsypkin (1979, 1980) proposed a robust recursive identification method analogous to the recursive least squares method. It follows the idea of Huber's maximum-likelihood-type estimator (M-estimator), which seeks for a minimax solution, i.e., an estimator minimizing the maximum asymptotic variance over some prescribed convex class to which the underlying distribution of innovations belongs. Its convergence properties for dynamic system identification have not been discussed thoroughly because of the introduction of some approximations in the identification method and correlation between observations. In this paper, convergence analysis of the robust recursive identification method is discussed for autoregressive models. Two theorems on convergence properties of the robust identification method are presented and proved by using the ODE approach and martingale convergence theory.