On Some Classes of Optimal Control Problem with State Constraints

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A Borel measure Lagrange multiplier appears in the maximum principle for state constrained problems. The question of continuity or absolute continuity of the measure-multiplier is highly relevant for various applications in particular for some problems of kinematic control. The velocity in such problems is considered as a state variable. As soon as the magnitude of the velocity is bounded, for instance above, (which is quite natural in problems of kinematic control), this leads to the state constraints and to a measure Lagrange multiplier in the necessary optimality conditions. In Control Theory, the methods that are use to solve these conditions often require the continuity of the measure. In this paper, we consider some examples of optimal control problems with state constraints for which one can ensure that this measure is continuous, without a calculation of extremal process.

About the authors

A V Gorbacheva

Peoples’ Friendship University of Russia

Email: avgorbacheva@inbox.ru
Department of nonlinear analysis and optimization; Department of applied mathematics Russian state social university 4, Wilhelm Pieck str., Moscow, Russia, 129226

D Yu Karamzin

Dorodnicyn Computing Centre of the Russian Academy of Science

Email: Dmitry_karamzin@mail.ru


Copyright (c) 2016 Горбачева А.В., Карамзин Д.Ю.

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