Simao P. S. Santos, Natalia Martins, Delfim F. M. Torres
Published 2015-07-21Version 1
We approach higher-order variational problems of Herglotz type from an optimal control point of view. Using optimal control theory, we derive a generalized Euler-Lagrange equation, transversality conditions, a DuBois-Reymond necessary optimality condition and Noether's theorem for Herglotz's type higher-order variational problems, valid for piecewise smooth functions.
Comments: This is a preprint of a paper to appear in 'Discrete and Continuous Dynamical Systems', Supplement dedicated to the Proceedings of the 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications. Submitted 15-Sept-2014; accepted for publication, subject to a revision as suggested by the referees, 17-Jul-2015; revised 21-Jul-2015. arXiv admin note: text overlap with arXiv:1412.0433
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