Noether currents for higher-order variational problems of Herglotz type with time delay

Simão P. S. Santos; Natália Martins; Delfim F. M. Torres

doi:10.3934/dcdss.2018006

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2018, Volume 11, Issue 1: 91-102. Doi: 10.3934/dcdss.2018006

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Noether currents for higher-order variational problems of Herglotz type with time delay

Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

* Corresponding author: N. Martins
* Corresponding author: N. Martins

Received: August 31, 2016

Revised: February 28, 2017

Published: February 2018

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Abstract

We study, from an optimal control perspective, Noether currents for higher-order problems of Herglotz type with time delay. Main result provides new Noether currents for such generalized variational problems, which are particularly useful in the search of extremals. The proof is based on the idea of rewriting the higher-order delayed generalized variational problem as a first-order optimal control problem without time delays.

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Mathematics Subject Classification: Primary: 49K15, 49S05; Secondary: 49K05, 34H05.

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