An Optimal Control Approach to Herglotz Variational Problems

Abstract

We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary optimality condition and Noether's theorem for Herglotz's fundamental problem, valid for piecewise smooth functions.

This is a preprint of a paper whose final and definite form will be published in Springer Communications in Computer and Information Science (CCIS), ISSN 1865-0929. Paper submitted 3/Aug/2014; revised 26/Nov/2014; accepted for publication 27/Nov/2014