A classification-based approach to the optimal control of affine switched systems

This paper deals with the optimal control of discrete–time switched systems, characterized by a finite set of operating modes, each one associated with given affine dynamics. The objective is the design of the switching law so as to minimize an infinite–horizon expected cost, that penalizes frequent switchings. The optimal switching law is computed off–line, which allows an efficient online operation of the control via a state feedback policy. The latter associates a mode to each state and, as such, can be viewed as a classifier. In order to train such classifier–type controller one needs first to generate a set of training data in the form of optimal state–mode pairs. In the considered setting, this involves solving a Mixed Integer Quadratic Programming (MIQP) problem for each pair. A key feature of the proposed approach is the use of a classification method that provides guarantees on the generalization properties of the classifier. The approach is tested on a multi–room heating control problem.