Discrete mechanics and mixed integer optimal control of dynamical systems

Mixed integer optimal control problems are a generalization of ordinary optimal control problems that include additional integer valued control functions. The integer control functions are used to switch instantaneously from one system to another. We use a time transformation (similar as in [1]) to get rid of the integer valued functions. This allows to apply gradient based optimization methods to approximate the mixed integer optimal control problem. The time transformation from [1] is adapted such that problems with distinct state domains for each system can be solved and it is combined with the direct discretization method DMOC [2,3] (Discrete Mechanics and Optimal Control) to approximate trajectories of the underlying optimal control problems. Our approach is illustrated with the help of a first example, the hybrid mass oscillator. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)