# Noether currents for higher-order variational problems of Herglotz type with time delay

## TL;DR

This paper develops new Noether currents for higher-order Herglotz variational problems with time delay by reformulating them as delay-free first-order optimal control problems, aiding in finding extremals.

## Contribution

It introduces a novel approach to derive Noether currents for complex delayed variational problems by transforming them into simpler control problems.

## Key findings

- New Noether currents for delayed higher-order variational problems
- Reformulation technique simplifies the search for extremals
- Enhanced understanding of symmetries in delayed systems

## Abstract

We study, from an optimal control perspective, Noether currents for higher-order problems of Herglotz type with time delay. Main result provides new Noether currents for such generalized variational problems, which are particularly useful in the search of extremals. The proof is based on the idea of rewriting the higher-order delayed generalized variational problem as a first-order optimal control problem without time delays.