ИСТИНА

We consider a class of optimal control problems with a scalar state constraint. Studied problem involves "inertial" of prescribed order dynamics for constrained state variable. For a trajectory with a smooth contact (of order corresponding to inertial delay" order) with a single boundary subarc, we first obtain, using a special technique (two-stage variation approach), optimality conditions in the form of Gamkrelidze, and then obtain the full set of optimality conditions in the Dubovitskii-Milyutin form, including the nonnegativity of the measure density and its atoms at the junction points.