By means of some simple examples from economics, we elucidatecertain solution tools for the solution of optimal control problems were the system under study undergoes major changes when certain boundaries are crossed. The major changes may be that the state gets a jump discontinuity when...

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...

In an in_nite horizon optimal control problem, the Hamiltonian vanishes at the in_nite horizon, when the di_erential 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...