Optimizing Hybrid Control Trajectories by Model abstraction and Refinement

Techniques for optimal control of hybrid systems have to consider the complex interaction of continuous and discrete dynamics and are required to limit the computational complexity arising from the corresponding search spaces. This contribution proposes an approach to computing hybrid optimal control trajectories based on an iterative model-abstraction and refinement scheme. The hybrid automaton is mapped to an abstract representation which is enriched by cost information gained from graph. Candidate solutions are computed on the abstract level and are mapped back to the level of the hybrid model, where they are validated. A refinement step guides the search for (sub-) optimal hybrid control trajectories. The proposed approach is implemented for the optimization of the start-up procedure for a chemical reactor.