Robust identification of discrete-time stochastic systems

Abstract

Since a real system can hardly be modelled by an exact linear deterministic or stochastic system and in this case a small disturbance may cause instability of adaptive algorithms (Egardt, 1980,Riedle et al 1984,Rohrs,1982),it is of great importance to analyse the influence of the unmodelled dynamics contained in the system upon the behavior of the adaptive control system. For recent years there has been a vast amount of research devoted to this issue (Anderson et al,1986,Bitmead et al,1986,Goodwin et al, 1985,Hili et al,1985,Ioannou et al 1984a,b,Ioannou et ai,1985 and Kosut et al 1984). The authors have analysed the robustness of identification and adaptive control algorithms in (Chen & Guo,1986a,b) for disCreteand continuous-time stochastic systems respectively,when the extended least squares (ELS) identification is applied. Roughly speaking,there it is shown that the estimation error and the deviation of the tracking error from its minimum value is small when the unmodelled dynamics is small in a certain sense. In this paper we are concentrated on the robustness issue of identification for the discrete-time stochastic system which consists of a modelled part being a CARMA process and of an unmodelled part On,i.e. the system is described by