Skip to main content

Stochastic control approach to the control of a forward parabolic equation, reciprocal process and minimum entropy

  • 2. Contributed Papers
  • Conference paper
  • First Online:
Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 185))

  • 175 Accesses

Abstract

We discuss relations between a controllability problem for a forward parabolic equation, a Jamison’s reciprocal process, a stochastic optimal control problem and a problem of minimum entropy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Blaquière, System Theory: A New Approach to Wave Mechanics, Journal of Optimization Theory and Applications, Vol. 32, No. 4, 1980.

    Google Scholar 

  2. A. Blaquière, Girsanov Transformation and two Stochastic Optimal Control Problems. The Schrödinger System and Related Controllability Results, in Modeling and Control of Systems in Engineering, Quantum Mechanics, Economics and Biosciences. Lecture Notes in Control and Information Sciences 121. Springer-Verlag Berlin Heidelberg 1989. (Proceedings of the Third Bellman Continuum Int. Workshop 1988).

    Google Scholar 

  3. A. Blaquière, “Controllability of a Fokker-Planck Equation, the Schrödinger System, and a Related Stochastic Optimal Control”, in Proceedings of the Fourth Workshop on Control Mechanics, January 22–23, 1991, University of Southern California, Los Angeles, California, Lecture Notes in Control and Information Sciences, Springer-Verlag Berlin Heidelberg (to appear).

    Google Scholar 

  4. A. Blaquière, Sufficiency Conditions for Existence of an Optimal Feedback Control in Stochastic Mechanics, Dynamics and Control Vol.1, No. 1, 7–24, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Blaquière, Controllability of a Fokker-Planck Equation, the Schrödinger System, and a Related Stochastic Optimal Control (Revised Version), to appear in Dynamics and Control Vol.2, No. 3, 235–253, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  6. I. Csiszar, 1-Divergence Geometry of Probability Distributions and Minimization Problems in The Annals of Probability, Vol. 3, No. 1, 146–158, 1975.

    MATH  MathSciNet  Google Scholar 

  7. D. Dawson, L. Gorostiza, and A. Wakolbinger, Shrödinger processes and large deviations, J. Math. Phys. 31 (10), 2385–2388, October 1990.

    Article  MATH  MathSciNet  Google Scholar 

  8. M.D. Donsker and S.R. Varadhan, Asymptotic Evaluation of Certain Markov Process Expectations for Large Time-III, Communications on pure and applied Mathematics, Vol. XXIX, 389–461, 1976.

    Article  MathSciNet  Google Scholar 

  9. W. H. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control, Springer-Verlag Berlin, 1975.

    MATH  Google Scholar 

  10. W. H. Fleming and Sheunn-Jyi Sheu, Stochastic Variational Formula for Fundamental Solutions of Parabolic PDE, Appl. Math. Optim. 13: 193–204, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  11. H. Föllmer, “Random fields and diffusion processes”, in Ecole d’été de Saint Flour XV–XVII (1985–1987), Lecture Notes in Mathematics 1362, Springer-Verlag Berlin, 1988.

    Google Scholar 

  12. B. Jamison, “Reciprocal Processes”, Z. Wahrscheinlichkeitstheorie ver. Gebiete 30, 65 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  13. K. Kime and A. Blaquière, From two Stochastic Optimal Control Problems to the Schrödinger Equation, in Modeling and Control of Systems in Engineering, Quantum Mechanics, Economics and Biosciences. Lecture Notes in Control and Information Sciences 121. Springer-Verlag Berlin Heidelberg 1989. (Proceedings of the third Bellman Continuum Int. Workshop 1988).

    Google Scholar 

  14. M. Pavon and A. Wakolbinger, “On Free Energy, Stochastic Control, and Schrödinger Processes”, Proceedings Workshop on Modeling and Control of Uncertain Systems, Birkhäuser, Boston, May 1991.

    Google Scholar 

  15. A. Wakolbinger, A Simplified Variational Characterisation of Schrödinger Processes, J. Math. Phys., 30, 2943, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  16. A. Wakolbinger, Schrödinger Bridges from 1931 to 1991, to appear in Proc. of IV CLAPEM, Mexico City.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

R. F. Curtain A. Bensoussan J. L. Lions

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag

About this paper

Cite this paper

Blaquière, A., Sigal-Pauchard, M. (1993). Stochastic control approach to the control of a forward parabolic equation, reciprocal process and minimum entropy. In: Curtain, R.F., Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems. Lecture Notes in Control and Information Sciences, vol 185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0115046

Download citation

  • DOI: https://doi.org/10.1007/BFb0115046

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56155-2

  • Online ISBN: 978-3-540-47480-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics