n an infinite horizon optimal control problem, the Hamiltonian vanishes at the infinite horizon, when the differential equation is autonomous. The integrand in the integral criterion may contain the time explicitly, but it has to satisfy certain integrability conditions. A generalization of...

Piecewise deterministic control problems are problems involving stochastic disturbance of a special type. In certain situations, in an otherwise deterministic control system, it may happen that the state jumps at certain stochastic points of time. Examples are sudden oil finds, or sudden...

Optimal nonanticipating controls are shown to exist in nonautonomous piecewise deterministic control problems with hard terminal restrictions. The assumptions needed are completely analogous to those needed to obtain optimal controls in deterministic control problems. The proof is based on...