On the convergence of the self-tuning algorithms based on nonmodified least-squares

Self-tuning servo control based on a nonmodified least-squares algorithm is considered. The fundamental result of the analysis is that the passivity of the two time-varying operators depending on the noise process dynamics, regression vector, and the ponderation matrix sequence of the algorithm is essential for the global stability of the self-tuning regulator. The methodology can be applied to problems of adaptive prediction based on a nonmodified least-squares algorithm and system parameter identification by a least-squares algorithm with a priori prediction.