Hysteresis-based switching control of stochastic linear systems

We study hysteresis-based switching control for a class of discrete-time stochastic linear systems. We take as given a family of candidate controllers that is sufficiently rich so as to include at least one controller suitable for each admissible process model. The controller operating in closed-loop with the system is replaced as soon as the measured data is significantly incompatible with the corresponding process model. In practice, this happens when the value taken by a least-squares identification cost exceeds its minimum (over all admissible models) by a certain hysteresis factor. The controller is then replaced by the one tuned to the best-fit model. We show that the proposed switching control system is stable for every value of the hysteresis factor, and that this is ensured despite of the presence of possibly unbounded noise.