Extending affine control policies to hybrid systems: Robust control of a DC-DC buck converter

Robust model predictive control involves determining constrained sequences of inputs to dynamical systems that maximize a certain objective under uncertain dynamics or constraints. Performing an optimization over open loop control inputs in such circumstances is known to lead to conservative input choices, leading to poor performance or even a failure to find a feasible input sequence. However, this conservativeness can be reduced by including recourse in the problem formulation. For linear systems with bounded disturbances, optimization over control laws that are affine in the disturbance measurements has emerged as a valid trade-off between performance and computational expense. In this paper we extend the idea of affine recourse to hybrid systems, and introduce an approach that chooses integer decision variables over the control horizon in conjunction with continuous decision variables that are subject to recourse. Using the example of a buck power converter, we illustrate the efficacy of our approach in comparison to an implementation of affine control policies based on a linearized model.