Adaptive Identification and Control of Linear Mimo Discrete Systems in a Noisy Environment

Abstract

An adaptive identification and control method for a linear Mlt10 (multi-input multi-output) discrete-time process is presented in this paper. A recursive identification algorithm, which is a multivariable extension of Landau'invarianza algorithm, is developed without using state measurements. The identifier is shown to give unbiased estimates in the presence of measurement noise. It is shown using Ljung's method that when the process operates in a stochastic environment, the parameters converge to their true values with probability one. The identification algorithm is then used in a control configuration, where the controller behaves as the adaptive inverse of the process and has as its input the desired output of the process. It is also shown, using a numerical example, that the method works effectively in the presence of input and measurement noises even for processes with slowly time varying parameters.