Noether's theorem for higher-order variational problems of Herglotz type

Abstract

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, DuBois–Reymond necessary optimality condition and Noether’s theorem for Herglotz’s type higher-order variational problems, valid for piecewise smooth functions.