Properties of extremals in optimal control problems with state constraints

An optimal control problem with state constraints is considered. Some properties of extremals to the Pontryagin maximum principle are studied. It is shown that, from the conditions of the maximum principle, it follows that the extended Hamiltonian is a Lipschitz function along the extremal and its total time derivative coincides with its partial derivative with respect to time. © 2016, Pleiades Publishing, Ltd.