Skip to main content
SpringerLink
Log in

The Method of Characteristics in an Identification Problem

  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

We consider the problem of identifying the parameters of a dynamic system from a noisy history of measuring the phase trajectory. We propose a new approach to the solution of this problem based on the construction of an auxiliary optimal control problem such that its extremals approximate the measurement history with a given accuracy. Using the solutions of the corresponding characteristic system, we obtain estimates for the residual, which is the difference between the coordinates of the extremals and the measurements of the phase trajectory. An estimate for the result of identifying the parameters of the dynamic system is obtained. An illustrative numerical example is given.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. B. T. Polyak, Introduction to Optimization (Nauka, Moscow, 1983; Optimization Software, New York, 1987).

    MATH  Google Scholar 

  2. Handbook of Automatic Control Theory, Ed. by A. Krasovskii (Nauka, Moscow, 1987) [in Russian].

    Google Scholar 

  3. N. N. Subbotina, E. A. Kolpakova, T. B. Tokmantsev, and L. G. Shagalova, The Method of Characteristics for Hamilton–Jacobi–Bellman Equations (Izd. UrO RAN, Yekaterinburg, 2013) [in Russian].

    Google Scholar 

  4. N. N. Subbotina and T. B. Tokmantsev, “Optimal synthesis to inverse problems of dynamics,” in Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, 2014 (Elsevier, New York, 2014), pp. 5866–5871.

    Google Scholar 

  5. A. V. Kryazhimskii and Yu. S. Osipov, “Modelling of a control in a dynamic system,” Engrg. Cybernetics 21 (2), 38–47 (1984).

    MathSciNet  Google Scholar 

  6. Yu. S. Osipov and A. V. Kryazhimskii, Inverse Problems for Ordinary Differential Equations: Dynamical Solutions (Gordon and Breach, London, 1995).

    MATH  Google Scholar 

  7. N. N. Krasovskii, Theory of Motion Control (Nauka, Moscow, 1968) [in Russian].

    Google Scholar 

  8. N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974) [in Russian].

    MATH  Google Scholar 

  9. A. N. Tikhonov, “On the stability of inverse problems,” C. R. (Doklady) Acad. Sci. URSS (N.S.) 39, 195–198 (1943).

    Google Scholar 

  10. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1961; Wiley, New York, 1962).

    Google Scholar 

  11. A. I. Subbotin, Generalized Solutions of First-Order Partial Differential Equations: The Dynamical Optimization Perspective (Birkhäuser, Boston, 1995; Inst. Komp. Issled., Moscow–Izhevsk, 2003).

    Google Scholar 

  12. N. N. Subbotina and E. A. Krupennikov, “Dynamic programming to identification problems,” World J. Eng. Technol. 4 (3B), 228–234 (2016).

    Article  Google Scholar 

  13. E. A. Krupennikov, “Validation of a solution method for the problem of reconstructing the dynamics of a macroeconomic system,” Trudy Inst. Mat. Mekh. UrO RAN 21 (2), 102–114 (2015).

    MathSciNet  Google Scholar 

  14. E. A. Barbashin, Introduction to the Theory of Stability (Nauka, Moscow, 1967) [in Russian].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990, Russia

    N. N. Subbotina & E. A. Krupennikov

  2. Ural Federal University, Yekaterinburg, 620002, Russia

    N. N. Subbotina & E. A. Krupennikov

Authors
  1. N. N. Subbotina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Krupennikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. N. Subbotina.

Additional information

Original Russian Text © N.N. Subbotina, E.A. Krupennikov, 2016, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Vol. 22, No. 2.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Subbotina, N.N., Krupennikov, E.A. The Method of Characteristics in an Identification Problem. Proc. Steklov Inst. Math. 299 (Suppl 1), 205–216 (2017). https://doi.org/10.1134/S008154381709022X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S008154381709022X

Keywords

Search

Navigation