Abstract
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.
Part of first author’s Ph.D. project, which is carried out under the Doctoral Programme in Mathematics (PDMat) of University of Aveiro.
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Acknowledgments
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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Santos, S.P.S., Martins, N., Torres, D.F.M. (2015). An Optimal Control Approach to Herglotz Variational Problems. In: Plakhov, A., Tchemisova, T., Freitas, A. (eds) Optimization in the Natural Sciences. EmC-ONS 2014. Communications in Computer and Information Science, vol 499. Springer, Cham. https://doi.org/10.1007/978-3-319-20352-2_7
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DOI: https://doi.org/10.1007/978-3-319-20352-2_7
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