A maximum principle for free endtime optimal control problems with data discontinuous in time

Recently, a maximum principle has been proved for free-endtime problems when the dynamics and the control constraint set are assumed to be merely measurable with respect to the time variable. A new simple derivation of this optimality condition is given from standard fixed-endtime results. It involves a generalization of the customary boundary condition on the maximized Hamiltonian function, evaluated along the optimal state trajectory and costate function. The hypotheses under which the maximum principle is proved permit unilateral state constraints, data merely Lipschitz continuous in the state variable, and endpoint constraints expressed as general set inclusions. The primary concern is with methodology and setting down a simple proof of the maximum principle for problems with data measurable in the time variable