Optimal control of systems with multiple steady-states

  • E. J. Doedel
  • M. C. Duban
  • G. Joly
  • J. P. Kernevez
Session 11 Numerical Methods
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 63)


This paper describes algorithms for the optimal control of multistate systems. As a test problem we use the reaction diffusion equation governing the steady-states of an enzyme system. The originality of such problems is that the state is not uniquely defined as a function of the control.


Optimal Control Problem Limit Point Conjugate Gradient Method Penalty Method Reaction Diffusion Equation 
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  1. [1]
    BANKS H.T., DUBAN M.C. and KERNEVEZ J.P., Optimal control of diffusion-reaction systems, p 47–59 in "Applied nonlinear analysis", edited by V. Lakshmikantham, Academic Press, 1979.Google Scholar
  2. [1]
    BOURGAT, Personal communicationGoogle Scholar
  3. [1]
    DOEDEL E.J., AUTO: a program for the automatic bifurcation analysis of autonomous systems, congressus numerantium, vol. 30 (1981) p 265–284.Google Scholar
  4. [2]
    DOEDEL E.J., Continuation techniques in the study of chemical reaction schemes, to appear in: Proc. Special Year on Energy Math., Univ. of Wyoming, K.I. Gross, ed. SIAM Publ.Google Scholar
  5. [1]
    FORTIN M. et GLOWINSKI R., Méthodes de Lagrangien augmenté. Collection MMI no 9, Paris, Dunod (1982).Google Scholar
  6. [1]
    KERNEVEZ J.P., Enzyme mathematics, North Holland, Amsterdam, 1980 X-262 pages.Google Scholar
  7. [2]
    KERNEVEZ J.P., Optimal control of multistate systems, in Encyclopedia of systems and control, editor in chief: Prof. Madan Singh, Pergamon Press Ltd, Oxford.Google Scholar
  8. [1]
    KERNEVEZ J.P., JOLY G. and SHARAN M., Control of systems with multiple steady-states, p 635–649 in Computing methods in applied sciences and engineering, North Holland, Amsterdam, 1982.Google Scholar
  9. [1]
    KERNEVEZ J.P. and LIONS J.L., Book to appear.Google Scholar
  10. [1]
    KUBICEK M., Dependence of solution of nonlinear systems on a parameter, ACM Transactions on mathematical software, vol. 2, no 1, March 1976, p 98–107.Google Scholar
  11. [1]
    LIONS J.L., Some methods in the mathematical analysis of systems and their control, Science Press, Beijing (1981).Google Scholar
  12. [2]
    LIONS J.L., Contrôle des systèmes distribués singuliers, Gauthier Villars, Paris, 1983.Google Scholar
  13. [3]
    LIONS J.L., Personal communication.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • E. J. Doedel
    • 1
  • M. C. Duban
    • 2
  • G. Joly
    • 2
  • J. P. Kernevez
    • 2
  1. 1.Computer ScienceConcordia UniversityMontrealCanada
  2. 2.U.T.C.CompiègneFrance

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