Sensitivity relations for the Mayer problem of optimal control

International audienceIn optimal control, sensitivity relations associate to a minimizing trajectory x(.) a pair of mappings formed by the Hamiltonian and the dual arc, that are selections from the generalized gradient of the value function at (t, x(t)) for each time t. In this paper we prove such sensitivity relations for the Mayer optimal control problem with dynamics described by a differential inclusion. If the associated Hamiltonian is semiconvex with respect to the state variable, then we show that sensitivity relations hold true for any dual arc associated to an optimal solution, instead of more traditional statements about the existence of a dual arc satisfying such relations