Constants of motion for Isoperimetric Variational Problems with Time   Delay
  In the present work, we obtain the constants of motion for isoperimetric variational problems with time delay. We consider a constrained optimization problem where the Lagrangian function defining the functional depends on time delayed arguments. We prove the isoperimetric Euler--Lagrange and DuBois--Reymond type optimality conditions and, in order to investigate the constants of motion for this problem, we obtain a nonsmooth extension of Noether's symmetry theorem for isoperimetric variational problems with delayed arguments. 
G. S. F. Frederico, M. J. Lazo, M. N. F. Barreto and J. Paiva
math.OC