Hight-order Noether's Theorem for Nonsmooth Extremals of Isoperimetric Variational Problems with Time Delay

Abstract

We obtain a nonsmooth higher-order extension of Noether's symmetry theorem for variational isoperimetric problems with delayed arguments. The result is proved to be valid in the class of Lipschitz functions, as long as the delayed higher-order Euler--Lagrange extremals are restricted to those that satisfy the delayed higher-order DuBois--Reymond necessary optimality condition. The important case of delayed isoperimetric optimal control problems is considered as well.

This is a preprint of a paper submitted in Applied Mathematics Letters. arXiv admin note: substantial text overlap with arXiv:1212.4932, arXiv:1603.02335

References in corpus (5)

• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations
• Noether's Theorem on Time Scales
• Noether's symmetry theorem for nabla problems of the calculus of variations
• Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
• Constants of motion for Isoperimetric Variational Problems with Time Delay