Optimal control of systems with time-driven and event-driven dynamics

We study a class of optimal control problems arising in hybrid systems, i.e., systems combining time-driven and event-driven dynamics. The problem structure is similar to a usual discrete-time optimal control problem except that, the index counts asynchronously occurring events and not synchronized time steps, and the dynamics contain the nonsmooth `max´ function. Variational techniques combined with nonsmooth analysis are used to develop the necessary conditions for optimality, and structural properties of optimal controls which can be used to develop numerical algorithms are derived