Hybrid Optimal Control of Motorized Traveling Salesmen and Beyond

Numerical methods for optimal control of hybrid dynamical systems are considered where the discrete dynamics and the nonlinear continuous dynamics are tightly coupled. A decomposition approach for numerically solving general mixed-integer continuous optimal control problems (MIOCPs) is discussed. In the outer optimization loop a branch-and-bound binary tree search is used for the discrete variables. The multiple-phase optimal control problems for the continuous state and control variables in the inner optimization loop are solved by a sparse direct collocation transcription method. A genetic algorithm is applied to improve the performance of the branch-and-bound approach by providing a good initial upper bound on the MIOCP performance index. Results are presented for motorized traveling salesmen problems, new benchmark problems in hybrid optimal control.