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.