On necessary boundary conditions for strongly optimal control in infinite horizon control problems

In the paper we consider the infinite horizon control problems in the free end case. We obtain the necessary conditions of strong optimality. The method of the proof actually follows the classic paper by Halkin, and the boundary condition for infinity that we construct in our paper is a stronger variety of the Seierstad condition. The complete system of relations of the maximum principle that was obtained in the paper allows us to write the expression for the adjoint variable in the form of improper integral that depends only on the developing trajectory. S. M. Aseev, A. V. Kryazhimskii, and V. M. Veliov obtained the similar condition as a necessary condition for certain classes of control problems. As we note in our paper, the obtained conditions of strong optimality lead us to a redefined system of relations for sufficiently broad class of control problems. An example is considered.