Optimal control of hybrid autonomous systems with state jumps

In this paper, optimal control problems for hybrid autonomous systems with state jumps are studied. In particular, we focus on problems in which a prespecified sequence of active subsystems is given and propose an approach to finding the optimal switching instants. Specifically, the derivatives of the cost with respect to the switching instants are derived and nonlinear optimization techniques are used to locate the optimal switching instants. Using the approach, accurate numerical values of local optimal solutions can be obtained. An example illustrates the approach.