Optimal Control for Switched Systems with Pre-defined Order and Switch-Dependent Dynamics

The optimal control problem for switched systems, with a predefined order of switches, is considered. The differential equations may depend explicitly on previous switching instants, and the latter may be state dependent. The solution is based on the Calculus‐of‐Variations, which leads to a single two‐point boundary‐value problem. A new condition for the Hamiltonian jump at the switching instants is obtained. Simple numerical examples demonstrate the results.