Skip to main content
SpringerLink
Log in

Dynamic Reconstruction of System Disturbances Using Inaccurate Discrete Measurements of Phase Coordinates

  • Control in Deterministic Systems
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

This paper studies the dynamic reconstruction of unknown disturbances for a system of differential equations that is nonlinear in phase variables. In the case of imperfectly measured phase coordinates within the given intervals, we develop a reconstruction algorithm with the integration of the feedback control and optimal programmed control. The algorithm is stable against data noises and computational errors. An illustrative 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.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. N. Krasovskii and A. I. Subbotin, Position Differential Games (Nauka, Moscow, 1974).

    MATH  Google Scholar 

  2. A. V. Kryazhimskii and Yu. S. Osipov, “On control modeling in dynamical system,” Izv. Akad. Nauk SSSR, Tekh. Kibernet., No. 2, 51–60 (1983).

    Google Scholar 

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

    MATH  Google Scholar 

  4. Yu. S. Osipov, A. V. Kryazhimskii, and V. I. Maksimov, Methods of Dynamical Reconstruction of Inputs of Controlled Systems (UrO RAN, Ekaterinburg, 2011) [in Russian].

    MATH  Google Scholar 

  5. V. I. Maksimov, “Method of Lyapunov functions in problems of reconstruction of inputs of systems with aftereffect,” Sovrem. Mat. Prilozh., Nelineinaya Din. 26, 78–95 (2005).

    Google Scholar 

  6. Yu. S. Osipov, A. V. Kryazhimskii, and V. I. Maksimov, “Dynamic inverse problems for parabolic systems,” Differ. Equations 36, 643–661 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  7. V. I. Maksimov, Problems of Dynamical Reconstruction of Inputs of Infinite-Dimensional Systems (UrO RAN, Ekaterinburg, 2011) [in Russian].

    Google Scholar 

  8. A. V. Kryazhimskii and Yu. S. Osipov, “On methods of positional modeling of control in dynamical systems,” in Qualitative Questions of the Theory of Differential Equations and Controlled Systems (UrO AN SSSR, Sverdlovsk, 1988), pp. 34–44 [in Russian].

    Google Scholar 

  9. V. I. Maksimov, “Positional simulation of unlimited controls for nonlinear systems with dissipation,” Avtom. Telemekh., No. 4, 22–30 (1988).

    Google Scholar 

  10. V. I. Maksimov and L. Pandolfi, “On the reconstruction of unbounded controls in nonlinear dynamical systems,” Prikl. Mat. Mekh. 65 (3), 35–42 (2001).

    MathSciNet  MATH  Google Scholar 

  11. V. I. Maksimov, “Dynamical discrepancy method in the input reconstruction problem,” Comput. Math. Math. Phys. 44, 278 (2004).

    MathSciNet  Google Scholar 

  12. V. I. Maksimov, “The tracking of the trajectory of a dynamical system,” J. Appl. Math. Mech. 75, 667–674 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  13. A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  14. E. B. Lee and L. Markus, Foundations of Optimal Control Theory (Krieger, FL, 1986).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    V. I. Maksimov

  2. Ural Federal University, Yekaterinburg, 620075, Russia

    V. I. Maksimov

Authors
  1. V. I. Maksimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Maksimov.

Additional information

Original Russian Text © V.I. Maksimov, 2018, published in Izvestiya Akademii Nauk, Teoriya i Sistemy Upravleniya, 2018, No. 3, pp. 15–32.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maksimov, V.I. Dynamic Reconstruction of System Disturbances Using Inaccurate Discrete Measurements of Phase Coordinates. J. Comput. Syst. Sci. Int. 57, 358–373 (2018). https://doi.org/10.1134/S1064230718030061

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064230718030061

Search

Navigation