An approach for model predictive control of mixed integer-input linear systems based on convex relaxations

Model predictive control of systems with mixed discrete and continuous inputs usually requires the online solution of a mixed integer optimization problem. Optimal solutions of such problems require methods whose worst-case complexity is exponential in the number of binary variables. In this paper we propose an approximate approach in which the integer input constraints are initially relaxed. A projection is then applied to the relaxed solution in order to obtain inputs satisfying the integer constraints. Satisfaction of state constraints under the projected input sequence is to be guaranteed by applying a robust reformulation to the original relaxed problem. We restrict our approach here to the practically important class of Pulse-Width Modulated power electronic systems, and present a suitable projection function for such systems. We demonstrate an attractive trade-off between performance and computational cost, using the examples of a DC-DC buck converter and a single-phase AC-DC grid inverter.