Skip to main content
SpringerLink
Log in

Fixed point methods in nonlinear control

  • Conference paper
  • First Online:
Book cover Distributed Parameter Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 75))

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. Angell, T.S.: On controllability for nonlinear hereditary systems: a fixed-point approach, Nonlinear Anal., 4 (1980), pp. 529–545.

    Google Scholar 

  2. Bohnenblust, H.F., and Karlin, S.: On a theorem of Ville Contributions to the theory of games I, Annals of Mathematics Studies No. 24, Princeton Univ. Press, 1950, pp. 155–160.

    Google Scholar 

  3. Carmichael, N., Pritchard, A.J., and Quinn, M.D.: Nonlinear control and estimation in "Evolution equations and their applications, F. Kappel and W. Schappacher, Eds., Pitman 1982, pp. 30–51.

    Google Scholar 

  4. Carmichael, N., Pritchard, A.J., and Quinn, M.D.: State and parameter estimation for nonlinear systems, Appl. Math. & Opt., 9 (1982), pp. 133–161.

    Google Scholar 

  5. Carmichael, N., and Quinn, M.D.: Some ill-posed problems in control theory, Oberwolfach conference on ill-posed problems and regularisation techniques, September 1982.

    Google Scholar 

  6. Carmichael, N., and Quinn, M.D.: Joint state and parameter estimation 1982, J.P.L. conference on flexible satellite control, G. Rodriguez, Ed.

    Google Scholar 

  7. Carmichael, N.: Functional analysis and aspects of non-linear control theory, Ph.D. thesis, University of Warwick, 1982.

    Google Scholar 

  8. Curtain, R.F., and Pritchard, A.J.: Infinite dimensional linear systems theory, Lecture Notes in Control and Information Sciences, Vol. 8, Springer-Verlag, 1978.

    Google Scholar 

  9. Dacka, C.: On the controllability of a class of nonlinear systems, IEEE AC 25 (1980), pp. 263–266.

    Google Scholar 

  10. Dacka, C.: On the controllability of nonlinear systems with time-variable delays, IEEE AC 26 (1981), pp. 956–959.

    Google Scholar 

  11. Dauer, J.P.: A controllability technique for nonlinear systems, J. Math. Anal. Appl. 37 (1972), pp. 442–451.

    Google Scholar 

  12. Dauer, J.P.: Nonlinear perturbations of quasi-linear control systems, J. Math. Anal. Appl. 54 (1976), pp.

    Google Scholar 

  13. Davison, E.J., and Kunze, E.C.: Some sufficient conditions for the global and local controllability of nonlinear time varying systems, J. SIAM Contr., 8 (1970), pp.

    Google Scholar 

  14. Gahl, R.D.: Controllability of nonlinear systems of neutral type, J. Math. Anal. Appl. 63 (1978), pp. 33–42.

    Google Scholar 

  15. Hermes, H.: Controllability and the singular problem, J. SIAM Contr. 2 (1965), pp. 241–260.

    Google Scholar 

  16. Klamka, J.: On the global controllability of perturbed nonlinear systems, IEEE AC 20 (1975), pp. 170–172.

    Google Scholar 

  17. Klamka, J.: On the local controllability of perturbed nonlinear systems, IEEE AC 20 (1975), pp. 289–291.

    Google Scholar 

  18. Klamka, J.: Controllability of nonlinear systems with delay in control, IEEE AC 20 (1975), pp. 702–704.

    Google Scholar 

  19. Klamka, J.: Relative controllability of nonlinear systems with delays in control, Automatic, 12 (1976), pp.633–634.

    Google Scholar 

  20. Klamka, J.: Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE AC 21 (1976), 594–595.

    Google Scholar 

  21. Klamka, J.: Relative controllability of nonlinear systems with distributed delays in control, Int. J. Contr. 28 (1978), pp. 307–312.

    Google Scholar 

  22. Klamka, J.: Controllability of nonlinear systems with distributed delays in control, Int. J. Contr. 31 (1980), pp. 811–819.

    Google Scholar 

  23. Kuang-Chung Wei: A class of controllable nonlinear systems, IEEE AC 21 (1976), pp. 787–789.

    Google Scholar 

  24. Kartsatos, A.G.: Global controllability of perturbed quasi-linear systems, Problems of Contr. & Inf. Thy., 3 (1974), pp. 137–145.

    Google Scholar 

  25. Magnusson, K., Pritchard, A.J., and Quinn, M.D.: The applications of fixed point theorems to global nonlinear controllability problems, Proc. Semester on control theory, Warsaw, Poland, 1981.

    Google Scholar 

  26. Mirza, K., and Womack, B.F.: On the controllability of a class of nonlinear systems, IEEE AC 17 (1972), pp. 531–535.

    Google Scholar 

  27. Mirza, K., and Womack, B.F.: On the controllability of nonlinear time-delay systems, IEEE AC 17 (1972), pp. 812–814.

    Google Scholar 

  28. Nistri, P.: Periodic control problems for a class of nonlinear periodic differential systems, Nonlinear Anal. 7 (1983), pp. 79–90.

    Google Scholar 

  29. Seidman, T., and Hong-Xing Zhou: Existence and uniqueness of optimal controls for a quasi-linear parabolic equation, J. SIAM Contr. 20 (1982), pp. 747–762.

    Google Scholar 

  30. Seidman, T.: Two results on exact boundary control of parabolic equations, Applied Math. & Opt. 11 (1984), 145–152.

    Google Scholar 

  31. Smith, H.L., and Stuart, C.A.: A uniqueness theorem for fixed points, Proc. Amer. Math. Soc., 79 (1980), pp. 237–240.

    Google Scholar 

  32. Talman, L.A.: A note on Kellog's uniqueness theorem for fixed points, Proc. Amer. Math. Soc., 69 (1978), pp. 248–250.

    Google Scholar 

  33. Tarnove, I.: A controllability problem for nonlinear systems, Mathematical Thy. of Control, A.V. Balakrishnan and L.W. Neustadt, Eds., Academic Press 1967, pp. 170–179.

    Google Scholar 

  34. Yamamoto, Y.: Controllability of nonlinear systems, J.O.T.A. 22 (1977), pp. 41–49.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shell Research, Rijswijk, The Netherlands

    N. Carmichael

  2. Department of Mathematical Sciences, Sheffield City Polytechnic, United Kingdom

    M. D. Quinn

Authors
  1. N. Carmichael
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. D. Quinn
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Franz Kappel Karl Kunisch Wilhelm Schappacher

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Carmichael, N., Quinn, M.D. (1985). Fixed point methods in nonlinear control. In: Kappel, F., Kunisch, K., Schappacher, W. (eds) Distributed Parameter Systems. Lecture Notes in Control and Information Sciences, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0005643

Download citation

  • DOI: https://doi.org/10.1007/BFb0005643

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15872-1

  • Online ISBN: 978-3-540-39661-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation