Mixed-integer formulations for optimal control of piecewise-affine systems

Abstract

In this paper we study how to formulate the optimal control problem for a piecewise-affine dynamical system as a mixed-integer program. Problems of this form arise typically in hybrid Model Predictive Control (MPC), where at every time step an open-loop optimal control sequence is computed via numerical optimization and applied to the system in a moving horizon fashion. Not surprisingly, the efficiency in the formulation of the underlying mathematical program has a crucial influence on computation times, and hence on the applicability of hybrid MPC to high-dimensional systems.