Skip to main content
SpringerLink
Log in

Relaxed controls for stochastic boundary value problems in infinite dimension

  • Conference paper
  • First Online:
Optimal Control of Partial Differential Equations

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 149))

Abstract

The paper deals with the question of boundary controls for a class of linear abstract stochastic initial boundary value problems. The objective is to control the mean state trajectory and the corresponding covariance operator in the presence of both boundary and distributed noiscs. Both existence of optimal relaxed controls and necessary conditions of optimality are presented. The question of practical realization of relaxed controls is briefly discussed as closing remarks.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Amann, Parabolic evolution equations with nonlinear boundary conditions, Nonlinear Functional Analysis and Applications, Proc. Symp. Pure Math. Vol. 45, no 1, A.M.S., pp. 17–27, 1986.

    Google Scholar 

  2. N.U. Ahmed, Optimization and identification of systems governed by evolution equations on Banach space, Pitman Research Notes in Mathematics, Vol. 184, Longman Scientific and Technical, UK and John Wiley and Sons, New York, 1988.

    Google Scholar 

  3. N.U. Ahmed, Abstract stochastic evolution equations and related control and stability problems, Lecture Notes in Control and Information Sciences, Springer-Verlag, Vol 97, pp. 107–120, 1987.

    Google Scholar 

  4. N.U. Ahmed, Stochastic initial boundary value problems for a class of second order evolution equations, Proc. Int. Conf. on Theory and Applications of Differential Equations, (Ed. A.R. Aftabi Zadeh), Vol 1, Ohio Univ. Press, pp. 13–19, 1988.

    Google Scholar 

  5. N.U. Ahmed, Abstract stochastic evolution equations on Banach spaces, Journal of Stochastic Analysis and Applications, 3, 4, pp. 397–432, 1985.

    Google Scholar 

  6. N.U. Ahmed, Stability of limit measures induced by stochastic differential equations on Hilbert space, (invited paper, 29th CDC, Honolulu, Dec. 1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Ottawa, Canada

    N. U. Ahmed

Authors
  1. N. U. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Karl-Heinz Hoffmann Werner Krabs

Additional information

Dedicated to Professor L. Cesari

Rights and permissions

Reprints and permissions

Copyright information

© 1991 International Federation for Information Processing

About this paper

Cite this paper

Ahmed, N.U. (1991). Relaxed controls for stochastic boundary value problems in infinite dimension. In: Hoffmann, KH., Krabs, W. (eds) Optimal Control of Partial Differential Equations. Lecture Notes in Control and Information Sciences, vol 149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043210

Download citation

  • DOI: https://doi.org/10.1007/BFb0043210

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53591-1

  • Online ISBN: 978-3-540-46883-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation