Adaptive Input Design for Robust Identification of Output-constrained OE Models

Abstract

A robust identification of output error (OE) models with optimal input design for a case of constrained output variance is considered in this paper. In a case when observations have Gaussian mixture distributions, it is shown that the proposed robust algorithm for identification of OE models with constrained output, which is based on Huber’s function, will give more accurate results in relation to the classical linear algorithm. In a form of the theorem, it is shown that an optimal input signal can be achieved by a minimum variance controller whose reference is a white noise. The essential problem is that the optimal input depends on the system parameters to be identified. In order to overcome this problem, a two-stage adaptive procedure is proposed, where iterations are alternately carried out between parameter estimation and experiment design using the current parameter estimates. It is shown that such obtained excitation signals result in a significant increasing in a convergence rate. Theoretical results are illustrated by simulations.