On bilinear estimation and control

Abstract

Discrete single-input single-output bilinear systems with constant parameters are considered. First, the minimum variance regulator for known parameters is determined. Then the least squares parameter estimation method is applied and is seen to have certain desirable properties. Finally, the least squares parameter estimator is combined with the minimum variance regulator for the estimated model to produce a bilinear self-tuning regulator «BLSTR’. It is found that though the estimation may be biased, under certain assumptions, the BLSTR will converge to the minimum variance control law.