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We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives., Comment: Submitted 26/Jul/2009; Revised 04/Aug/2010; Accepted 09/Aug/2010; for publication in "Applied Mathematics Letters"

We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and previous results in the literature obtained as particular cases. As an application of the results of the paper we give necessary and sufficient Pareto optimality conditions for delta-nabla bi-objective optimal control problems., Comment: Preprint version of an article submitted 28-Nov-2009; revised 02-Jul-2010; accepted 20-Jul-2010; for publication in Journal of Vibration and Control

The calculus of variations on time scales is considered. We propose a new approach to the subject that consists in applying a differentiation tool called the contingent epiderivative. It is shown that the contingent epiderivative applied to the calculus of variations on time scales is very useful: it allows to unify the delta and nabla approaches previously considered in the literature. Generalized versions of the Euler-Lagrange necessary optimality conditions are obtained, both for the basic problem of the calculus of variations and isoperimetric problems. As particular cases one gets the recent delta and nabla results., Comment: Submitted 06/March/2010; revised 12/May/2010; accepted 03/July/2010; for publication in "Optimization---A Journal of Mathematical Programming and Operations Research"

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