Many discrete optimal control problems feature combinatorial constraints on the possible switching patterns, a common example being minimum dwell-time constraints. After discretizing to a finite time grid, for these and many similar types of constraints, it is possible to give a description of the convex hull of feasible (finite-dimensional) binary controls via extended formulations. In this work, we aim to transfer a large class of such descriptions to function space, by determining extended formulations for the closed convex hull of feasible control functions. Such an infinite-dimensional grid-independent convex-hull description can serve as a recipe for the practitioner for obtaining tight formulations for any discretization. Our result applies to a large class of constraints that follow a certain modular principle, described by a generalization of finite-state automata to infinite-dimensional input data, which we specifically define for this purpose.
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View Extended Formulations for Control Languages Defined by Finite-State Automata