Optimization of Boundary Value Problems for Certain Higher-Order Differential Inclusions

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Abstract

The present paper studies a new class of problems of optimal control theory with special differential inclusions described by higher-order linear differential operators (HLDOs). There arises a rather complicated problem with simultaneous determination of the HLDOs and a Mayer functional depending of high-order derivatives of searched functions. The sufficient conditions, containing both the Euler-Lagrange and Hamiltonian type inclusions and “transversality” conditions at the endpoints t = − 1, 0 and t = 1 are derived. One of the key features in the proof of sufficient conditions is the notion of locally adjoint mappings. Then, we demonstrate how these conditions can be transformed into Pontryagin’s maximum principle in some particular cases.

Keywords

Euler-Lagrange Set-valued Linear differential operators Boundary value conditions Transversality 

Mathematics Subject Classification 2010

34A60 49J15 49K15 65J10 
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Notes

Acknowledgments

The author would like to thank the Co-Editor, Prof. Khai T. Nguyen of the Journal of “Journal of Dynamical and Control Systems” and anonymous reviewers for their careful reading of the manuscript and their many insightful comments and suggestions.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIstanbul Technical UniversityIstanbulTurkey
  2. 2.Azerbaijan National Academy of SciencesInstitute of Control SystemsBakuAzerbaijan

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