Skip to main content

A new approach to the L-Q-R problem for hyperbolic dynamics with boundary control

  • Conference paper
  • First Online:
Distributed Parameter Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 102))

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. Bellman, R., Functional equations in the theory of dynamic programming, positivity and quasilinearity, Proc. Nat. Acad. Sci. U.S.A., 41 (1955), pp 743–746.

    Google Scholar 

  2. Balakrishnan, A.V., Applied Functional Analysis, Springer-Verlag, New York, 1976.

    Google Scholar 

  3. Da Prato, G., Quelques resultats d'existence unicité et regularité pour un probleme de la theorie du controle, J. Math. Pures et Appl. 52 (1973), pp. 353–375.

    Google Scholar 

  4. Da Prato, G., Lasiecka, I., Triggiani, R., A direct study of the Riccat equation arising in hyperbolic boundary control problems, submitted.

    Google Scholar 

  5. Fattorini, H.O., Ordinary differential equations in linear topological spaces, I and II, J. Differential Equations 5 (1968), pp. 72–105, and 6 (1969), pp. 50–70

    Google Scholar 

  6. Flandoli, F., On the optimal control of non well posed systems with boundary control, Proc. 2nd Int. Conf. on Distributed Parameter Systems, Springer-Verlag, Berlin, 1985.

    Google Scholar 

  7. Flandoli, F., Dynamic programming approach to the optimal control of systems governed by non well posed Cauchy problems in Hilbert spaces, Boll. U.M.I. (6), 5-B (1986), pp. 177–195.

    Google Scholar 

  8. Flandoli, F., Riccati equation arising in the boundary control of stochastic hyperbolic systems, Stochastic Anal. Appl. 4 (2), (1986), pp. 131–150.

    Google Scholar 

  9. Lasiecka, I., Lions, J.L., Triggiani, R., Non-homogeneous boundary value problems for second order hyperbolic operators, J. Math. Pures et Appl., to appear.

    Google Scholar 

  10. Lasiecka, I., Triggiani, R., A cosine operator approach to modeling L2(O,T;L2(Γ))-boundary input hyperbolic equations, Appl. Math. Optim. 7 (1981), pp. 35–93.

    Google Scholar 

  11. Lasiecka, I., Triggiani, R., Regularity of hyperbolic equations under L2(O,T;L2(Γ))-Dirichlet boundary terms, Appl. Math. Optim. 10 (1983), pp. 275–286.

    Google Scholar 

  12. Lasiecka, I., Triggiani, R., Riccati equations for hyperbolic partial differential equations with L2(O,T;L2(Γ))-Dirichlet boundary controls, SIAM J. Control Optim., to appear.

    Google Scholar 

  13. Lions, J.L., Magenes, E., Nonhomogeneous Boundary Value Problems and Applications, vol. I, Springer-Verlag, Berlin, 1972.

    Google Scholar 

  14. Tanabe, H., Equation of Evolution, Pitman, London, 1979.

    Google Scholar 

  15. Yosida, K., Functional Analysis, Springer-Verlag, Berlin, 1965.

    Google Scholar 

  16. Wonham, W.M., On a matrix riccati equation of stochastic control, SIAM J. Control 6 (1968), pp. 681–697.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Franz Kappel Karl Kunisch Wilhelm Schappacher

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Flandoli, F. (1987). A new approach to the L-Q-R problem for hyperbolic dynamics with boundary control. In: Kappel, F., Kunisch, K., Schappacher, W. (eds) Distributed Parameter Systems. Lecture Notes in Control and Information Sciences, vol 102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0041984

Download citation

  • DOI: https://doi.org/10.1007/BFb0041984

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18468-3

  • Online ISBN: 978-3-540-47981-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics