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

2016/03/19 by Gastão S. F. Frederico, Frederico, G. S. F., Matheus J. Lazo +1
Engineering · Mathematics · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1603.06029

openalex publication_date 2016/03/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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