Skip to main content
Log in

Input Reconstruction in a Dynamic System from Measurements of a Part of Phase Coordinates

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

The unknown input disturbance in a system of nonlinear ordinary differential equations is reconstructed from measurements of some of the state coordinates. A solution algorithm is proposed that is robust to information noises and computational errors. The algorithm is constructed using guaranteed control theory.

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

Access this article

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

    MATH  Google Scholar 

  2. Yu. S. Osipov, A. V. Kryazhimskii, and V. I. Maksimov, Dynamic Reconstruction Methods for Inputs of Controlled Systems (Ural. Otd. Ross. Akad. Nauk, Yekaterinburg, 2011) [in Russian].

    MATH  Google Scholar 

  3. Yu. S. Osipov, F. P. Vasil’ev, and M. M. Potapov, The Basics of the Dynamic Regularization Method (Mosk. Gos. Univ., Moscow, 1999) [in Russian].

    Google Scholar 

  4. V. I. Maksimov, “Reconstruction of controls in exponentially stable linear systems subjected to small perturbations,” J. Appl. Math. Mech. 71 (6), 851–861 (2007).

    Article  MathSciNet  Google Scholar 

  5. V. I. Maksimov, “On one algorithm of input action reconstruction for linear systems,” J. Comput. Syst. Sci. Int. 48 (5), 681–690 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  6. Yu. S. Osipov, A. V. Kryazhimskii, and V. I. Maksimov, “Some algorithms for the dynamic reconstruction of inputs,” Proc. Steklov Inst. Math. 275, Suppl. 1, 86–120 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  7. M. S. Blizorukova and V. I. Maksimov, “An algorithm for dynamic reconstruction of input disturbances from observations of some of the coordinates,” Comput. Math. Math. Phys. 51 (6), 942–951 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  8. N. N. Krasovskii and A. I. Subbotin, Game-Theoretical Control Problems (Nauka, Moscow, 1974; Springer-Verlag, New York, 1988).

  9. F. P. Vasil’ev, Methods for Solving Optimization Problems (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  10. V. I. Maksimov, “Calculation of the derivative of an inaccurately defined function by means of feedback laws,” Proc. Steklov Inst. Math. 291, 219–231 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  11. V. I. Maksimov, “The tracking of the trajectory of a dynamical system,” J. Appl. Math. Mech. 75 (6), 667–674 (2011).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. I. Maksimov.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maksimov, V.I. Input Reconstruction in a Dynamic System from Measurements of a Part of Phase Coordinates. Comput. Math. and Math. Phys. 59, 708–717 (2019). https://doi.org/10.1134/S0965542519040122

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542519040122

Keywords:

Navigation