A unified approach to the calculus of variations on time scales

Details A unified approach to the calculus of variations on time scales A unified approach to the calculus of variations on time scales

2010-05-25

arxiv.org/abs/1005.4581v1

IEEE Catalog Number CFP1051D-CDR, 2010, 595--600

Mathematics

Optimization and Control

7 pages, presented at the 2010 Chinese Control and Decision Conference, Xuzhou, China, May 26-28, 2010

Scientific paper

10.1109/CCDC.2010.5498972

In this work we propose a new and more general approach to the calculus of variations on time scales that allows to obtain, as particular cases, both delta and nabla results. More precisely, we pose the problem of minimizing or maximizing the composition of delta and nabla integrals with Lagrangians that involve directional derivatives. Unified Euler-Lagrange necessary optimality conditions, as well as sufficient conditions under appropriate convexity assumptions, are proved. We illustrate presented results with simple examples.

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