The Hybrid Minimum Principle in the presence of switching costs

Hybrid optimal control problems are studied for systems where, in addition to running costs, switching between discrete states incurs costs. A key aspect of the analysis is the relationship between the Hamiltonian and the adjoint process before and after the switching instants. In this paper, the analysis is performed for systems for which autonomous and controlled state jumps are not permitted. First the results are established in the hybrid Mayer optimal control problem setup using the needle variation technique, and then the results for the hybrid Bolza optimal control problem are established via the calculus of variations methodology.