Cautious hierarchical switching control of stochastic linear systems

Standard switching control methods are based on the certainty equivalence philosophy in that, at each switching time, the supervisor selects the candidate controller that is better tuned to the currently estimated process model. If the estimated model does not appropriately describe the process, this procedure may result in the selection of a controller that is not appropriate for the actual process. In this paper, we propose a supervisory switching logic that takes into account the uncertainty on the process description when performing the controller selection. Specifically, a probability measure describing the likelihood of the different models is computed on-line based on the collected data and, at each switching time, the supervisor selects the candidate controller that, according to this probability measure, performs the best on the average. If the candidate controller set is hierarchically structured, the supervisor automatically selects the controller that appropriately compromises robustness and performance, given the actual level of uncertainty on the process description. The use of randomized algorithms makes the supervisor implementation computationally tractable.