On the Geometry of the Pontryagin Maximum Principle in Banach Spaces

Springer Science and Business Media LLC - Tập 23 - Trang 443-463 - 2015
M. I. Krastanov1,2, N. K. Ribarska1,3, Ts. Y. Tsachev3
1Faculty of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria
2Department of Biomathematics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
3Department of Operations Research, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

Tóm tắt

A basic idea of the classical approach to obtain necessary optimality conditions in the calculus of variations and optimal control is to perturb with suitable variations the reference trajectory and then compare the unperturbed value of the cost functional with the perturbed one. Here we compare several classes of variations for the study of infinite-dimensional optimal control problems. We prove an abstract result on a non-separation property of two closed sets and obtain as corollaries versions of the maximum principle under various assumptions. Illustrative examples indicating some limits of applicability of the existing variational techniques are presented.

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Springer Science and Business Media LLC

Tập 23

443-463

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