Robustness and convergence of least-squares identification and adaptive tracking for stochastic systems

The adaptive conlrol for tracking a stochastic reference signal based upon the extended least-squares algorithm estimating unknown parameters of the modelled part in a stochastic syslem is recursively defined. It is shown that the closed-loop system is stable: the estimation error decreases as the unmodelled dynamics decays and the tracking error differs from the minimum plus a small value when the unmodelled dynamics is bounded in the average sense; the strong consistency of the estimates and asymptotical optimality of adaptive tracking are obtained when the unmodelled dynamics approaches zero in the average sense.