An Optimal Control Approach to Herglotz Variational Problems

  • Simão P. S. Santos
  • Natália Martins
  • Delfim F. M. TorresEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 499)


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.


Herglotz’s variational problems Optimal control Euler–Lagrange equations Invariance Dubois–Reymond condition Noether’s theorem 



This work was supported by Portuguese funds through the Center for Research and Development in Mathematics and Applications (CIDMA), within project UID/MAT/04106/2013, and the Portuguese Foundation for Science and Technology (FCT). The authors would like to thank an anonymous Reviewer for valuable comments.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Simão P. S. Santos
    • 1
  • Natália Martins
    • 1
  • Delfim F. M. Torres
    • 1
    Email author
  1. 1.CIDMA–Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal

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