Initialization concepts for optimal control of hybrid systems

Indirect methods solve optimal control problems for hybrid systems with high precision, but they are difficult to initialize. To overcome the initialization difficulties, two different concepts based on direct methods are presented. In the first approach, the hybrid optimal control problem is solved by a direct method until the precision is sufficient for a successful initialization of the indirect method. The second approach decomposes the hybrid optimal control problem into non-hybrid subproblems, where each subproblem can be initialized separately by a direct method. This results in a significantly higher robustness of the initialization compared to the first approach. However, the precision of the solution with the indirect method achieved in the first approach is higher. The two concepts are compared in a numerical example.