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Hamiltonian structures in optimal control theory

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Abstract

The concept of a piecewise smooth Hamiltonian system, motivated by optimal control theory, is introduced and developed. It is proved that the Poisson bracket of two integrals of such a system is globally continuous. Integrable piecewise smooth systems are proved to be equivalent to smooth integrable systems.

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Author notes

  1. A. V. Pukhlikov

    Present address: Prospekt 60-letya Oktyabrya 9, Institute for Systems Analysis, 117312, Moscow, Russia

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    1. A. V. Pukhlikov
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    This research was partially supported by the Russian Foundation for Fundamental Research, grant No. 93-012-470

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    Pukhlikov, A.V. Hamiltonian structures in optimal control theory. Journal of Dynamical and Control Systems 1, 379–401 (1995). https://doi.org/10.1007/BF02269376

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