Optimal control of hybrid dynamic systems

The optimal control of hybrid systems is challenging as it adds resets of state variables as well as the combinatorics of discrete-event behavior to the optimization of continuous dynamics. This contribution first provides an overview of the most important methods for different variants of the hybrid optimal control problem. For a problem instance of discrete-time hybrid systems with continuous and discrete controls, the paper then proposes a new technique. In there, the optimal solution is approximated with relatively low computational effort by use of approximated cost bounds and an adjacancy criterion for explored states.