An Optimal Control Approach to Herglotz Variational Problems
  We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary optimality condition and Noether's theorem for Herglotz's fundamental problem, valid for piecewise smooth functions. 
Simao P. S. Santos, Natalia Martins, Delfim F. M. Torres
math.OC