Some algorithms for the dynamic reconstruction of inputs

  • Yu. S. Osipov
  • A. V. Kryazhimskii
  • V. I. Maksimov


For some classes of systems described by ordinary differential equations, a survey of algorithms for the dynamic reconstruction of inputs is presented. The algorithms described in the paper are stable with respect to information noises and computation errors; they are based on methods from the theory of ill-posed problems as well as on appropriate modifications of N.N. Krasovskii’s principle of extremal aiming, which is known in the theory of guaranteed control.


reconstruction control models 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974) [in Russian].MATHGoogle Scholar
  2. 2.
    N. N. Krasovskii, Control of a Dynamical System (Nauka, Moscow, 1985) [in Russian].Google Scholar
  3. 3.
    A. V. Kryazhimskii and Yu. S. Osipov, Engrg. Cybernetics 21(2), 38 (1984).MathSciNetGoogle Scholar
  4. 4.
    A. N. Tikhonov and V. Ya. Arsenin, Methods for Solving Ill-Posed Problems (Nauka, Moscow, 1979) [in Russian].Google Scholar
  5. 5.
    F. P. Vasil’ev, Methods for Solving Extremal Problems (Nauka, Moscow, 1981) [in Russian].MATHGoogle Scholar
  6. 6.
    V. I. Maksimov, Comput. Math. Math. Phys. 44(2), 278 (2004).MathSciNetGoogle Scholar
  7. 7.
    A. S. Mart’yanov, J. Comput. Syst. Sci. Int. 43(4), 542 (2004).MathSciNetGoogle Scholar
  8. 8.
    M. S. Blizorukova and A. M. Kodess, Differential Equations 44(11), 1512 (2008).CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    V. I. Maksimov, J. Comput. Syst. Sci. Int. 48(5), 681 (2009).CrossRefMathSciNetGoogle Scholar
  10. 10.
    V. I. Maksimov, J. Appl. Math. Mech. 70(5), 696 (2006).CrossRefMathSciNetGoogle Scholar
  11. 11.
    Yu. S. Osipov, in Number and Thought (Znanie, Moscow, 1987), Issue 10, pp. 7–27 [in Russian].Google Scholar
  12. 12.
    A. V. Kryazimskiy and V. I. Maksimov, J. Inv. Ill-Posed Problems 16(6), 587 (2008).CrossRefGoogle Scholar
  13. 13.
    P. A. Vanrolleghem and M. Van Daele, Water Science and Technology 30(4), 243 (1994).Google Scholar
  14. 14.
    J. D. Stigter, D. Vries, and K. J. Keesman, in Proc. of the European Control Conference (Cambridge, 2003), Paper 066.Google Scholar
  15. 15.
    K. J. Keesman and V. I. Maksimov, Internat. J. Control 81(1), 134 (2008).CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Yu. S. Osipov and A. V. Kryazhimskii, Inverse Problems for Ordinary Differential Equations: Dynamical Solutions (Gordon & Breach, London, 1995).MATHGoogle Scholar
  17. 17.
    V. I. Maksimov, in Modern Mathematics and Its Application: Optimal d]Control (VINITI, Moscow, 2001), Vol. 97, pp. 91–110 [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • Yu. S. Osipov
    • 1
  • A. V. Kryazhimskii
    • 2
    • 3
  • V. I. Maksimov
    • 4
    • 5
  1. 1.Presidium of the Russian Academy of SciencesMoscowRussia
  2. 2.Steklov Mathematical InstituteMoscowRussia
  3. 3.International Institute for Applied Systems AnalysisLaxenburgAustria
  4. 4.Institute of Mathematics and MechanicsUral Branch of the Russian Academy of SciencesYekaterinburgRussia
  5. 5.Ural Federal UniversityYekaterinburgRussia

Personalised recommendations