A variable time transformation method for mixed-integer optimal control problems

The article discusses a variable time transformation method for the approximate solution of mixed-integer non-linear optimal control problems (MIOCP). Such optimal control problems enclose real-valued and discrete-valued controls. The method transforms MIOCP using a discretization into an optimal control problem with only real-valued controls. The latter can be solved efficiently by direct shooting methods. Numerical results are obtained for a problem from automobile test-driving that involves a discrete-valued control for the gear shift of the car. The results are compared to those obtained by Branch&Bound and show a drastic reduction of computation time. This very good performance makes the suggested method applicable even for many discretization points.