On Bolza optimal control problems with constraints

We provide sufficient conditions for the existence and Lipschitz continuity of solutions to a constrained Bolza optimal control problem. The main feature of our problem is the unboundedness of the dynamics f(x,U) and the absence of superlinear growth conditions for the running cost L. Such classical assumptions are here replaced by conditions on the Hamiltonian that can be satisfied, for instance, by some Lagrangians with no growth. This paper extends our previous results in Existence and Lipschitz regularity of solutions to Bolza problems in optimal control to the state constrained case.