Pontryagin type conditions for differential inclusions with free time

AbstractOptimality conditions for differential inclusion problems, due to Kaskosz and Lojasiewicz, involve a costate equation and a pointwise maximizing property of the optimal velocity, expressed in terms of a Carathéodory selection of the differential inclusion. Such conditions have been extended in various directions, notably to permit unilateral state constraints. Here we add to earlier extensions, principally by allowing free endtimes. This is accomplished even though the data are required to be merely measurable in the time variable. The results are obtained by applying recent optimality conditions for free time problems, involving a Hamiltonian inclusion, to an auxiliary problem and a simple limiting argument