Abstract: Mixed-integer optimal control problems incorporate both the modeling capabilities of partial differential equations and discrete variables. We present an algorithm that is able to approximate the infima of a rich class of mixed-integer optimal control problems arbitrarily close. The method is very efficient because it only requires means to discretize and solve relaxed optimal control problems with continuous variables, and means to round continuously valued controls to discrete-valued controls in a subtle manner.

We propose to incorporate switching costs of the discrete controls into the framework to broaden the scope of applications and facilitate implementations in reality. To estimate the required constants of the involved discretization grids a priori, we propose to analyze control approximations in weak norms. Finally, we present a novel algorithmic idea to solve discretized relaxed continuous optimal control problems if additional mixed constraints are present.