On Stationarity Conditions in an Optimal Control Problem with a Simple Contact with the Phase Boundary

摘要

A certain class of optimal control problems with a one-dimensional phase constraint is considered. When a trajectory contacts the phase boundary on an interval, we employ a special procedure (two-stage variation) to obtain optimality conditions in the Gamkrelidze form and then in the Dubovitskii-Milyutin form, including the sign definiteness property measure density and its jumps at junction points.