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Controllability of a Forkker-Planck equation, the Schrodinger system, and a related stochastic optimal control

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Book cover Mechanics and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 170))

Abstract

We start from a controllability problem for a Fokker-Planck equation, termed Problem A. A solution (v*, φ*) to that problem is constructed via a Theorem of Jamison, under proper assumptions. Theorem 2 gives a sufficiency condition concerning the given initial and terminal data for that solution to exist. Theorem 3 states that v* is an optimal feedback control for a stochastic optimal control problem with constraint on the end-state, termed Problem B, and further v* corresponds to the minimum of an entropy distance. At last Problem A is transformed into a controllability problem for a stochastic differential equation, termed Problem C: the solution to Problem C corresponding to the one constructed in Problem A is the Markovian process satisfying the given end conditions in a set of reciprocal processes of Jamison.

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Authors and Affiliations

  1. Laboratoire d'Automatique Théorique, University Paris 7, Tour 14–24, 2 Place Jussieu, 75251, Paris Cedex 05, France

    A. Blaquière

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  1. A. Blaquière
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Janislaw M. Skowronski Henryk Flashner Ramesh S. Guttalu

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© 1992 Springer-Verlag

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Blaquière, A. (1992). Controllability of a Forkker-Planck equation, the Schrodinger system, and a related stochastic optimal control. In: Skowronski, J.M., Flashner, H., Guttalu, R.S. (eds) Mechanics and Control. Lecture Notes in Control and Information Sciences, vol 170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004305

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  • DOI: https://doi.org/10.1007/BFb0004305

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54954-3

  • Online ISBN: 978-3-540-46606-2

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