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## Archive of Issues

Russia Yekaterinburg
Year
2013
Issue
1
Pages
49-58
 Section Mathematics Title On necessary boundary conditions for strongly optimal control in infinite horizon control problems Author(-s) Khlopin D.V.a Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa Abstract 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. Keywords control problem, strong optimal control, infinite horizon problem, necessary conditions of optimality, transversality condition for infinity, Pontryagin maximum principle UDC 517.977.5 MSC 49K15, 49J45, 37N40 DOI 10.20537/vm130106 Received 11 February 2013 Language Russian Citation Khlopin D.V. On necessary boundary conditions for strongly optimal control in infinite horizon control problems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 1, pp. 49-58. References Aseev S.M., Kryazhimskii A.V. The Pontryagin maximum principle and optimal economic growth problems, Proc. Steklov Inst. Math., 2007, vol. 257, pp. 1–255. Aseev S.M., Besov K.O., Kryazhimskii A.V. Infinite-horizon optimal control problems in economics, Russ. Math. 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