Logic-based switching for the stabilization of stochastic systems in presence of unmodeled dynamics

We describe a supervisory control scheme for adaptively stabilizing an unknown discrete time linear system affected by a possibly unbounded noise. The scheme incorporates a switching logic mechanism, which, at adaptively selected event times, places in feedback with the system the controller designed for the model which is the best according to the least squares criterion. The event times are chosen so as to uniformly stabilize the estimated system. We show that, when the controller selection is based on a reduced order model of the system and the unmodeled dynamics is sufficiently small, the introduced switching scheme is successful in stabilizing the system. Moreover, in absence of unmodeled dynamics, we are also able to characterize the switching scheme performance in terms of a self-tuning result