Skip to main content
SpringerLink
Log in

Controllable dynamic systems and underdetermined systems of differential equations

  • Topical Issue
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The question is considered on the concept of a controllable dynamic system in the form of an underdetermined system of differential equations. The effectiveness of such a concept is shown for the solution of the problem of the classification of controllable systems.

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. Su, R., On Linear Equivalence of Nonlinear Systems, Syst. Control Lett., 1982, vol. 2, pp. 48–50.

    Article  MATH  Google Scholar 

  2. Hunt, L.R., Su, R., and Meyer, G., Global Transformations of Nonlinear Systems, IEEE Trans. Automat. Control, 1983, no. 1, pp. 24–31.

  3. Elkin, V.I., Reduktsiya nelineinykh upravlyaemykh sistem: differentsial’no-geometricheskii podkhod (Reduction of Nonlinear Controllable Systems: Differential-Geometric Approach), Moscow: Nauka, 1997.

    Google Scholar 

  4. Elkin, V.I., Subsystems of Controllable Systems and the Problem of Terminal Control, Autom. Remote Control, 1995, vol. 56, no. 1, part 1, pp. 16–22.

    MathSciNet  MATH  Google Scholar 

  5. Elkin, V.I., Reduction of Underdetermined Systems of Ordinary Differential Equations. I, Diff. Uravn., 2009, vol. 45, no. 12, pp. 1687–1697.

    MathSciNet  Google Scholar 

  6. Elkin, V.I., Reduction of Underdetermined Systems of Ordinary Differential Equations. II, Diff. Uravn., 2010, vol. 46, no. 11, pp. 1523–1535.

    MathSciNet  Google Scholar 

  7. Elkin, V.I., On Classification of Affine Controllable Systems with the Phase Space of Dimension of n < 4, Dokl. Akad. Nauk SSSR, 1988, vol. 302, no. 1, pp. 18–20.

    MathSciNet  Google Scholar 

  8. Elkin, V.I., Constructing Subsystems for Nonlinear Controlled Systems, Autom. Remote Control, 2010, vol. 71, no. 5, pp. 738–746.

    Article  MathSciNet  MATH  Google Scholar 

  9. Elkin, V.I., Affine Controllable Systems, Affine Distributions, and t-Codistributions, Diff. Uravn., 1994, vol. 30, no. 11, pp. 1869–1879.

    MathSciNet  Google Scholar 

  10. Elkin, V.I., On Categories and Bases of the Theory of Nonlinear Controllable Systems. V, Diff. Uravn., 2006, vol. 42, no. 11, pp. 1481–1489.

    MathSciNet  Google Scholar 

  11. Rashevskii, P.K., Geometricheskaya teoriya uravnenii s chastnymi proizvodnymi (Geometric Theory of Equations with Partial Derivatives), Moscow: Gostekhizdat, 1947.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, Russia

    V. I. Elkin

Authors
  1. V. I. Elkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.I. Elkin, 2011, published in Avtomatika i Telemekhanika, 2011, No. 9, pp. 28–38.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Elkin, V.I. Controllable dynamic systems and underdetermined systems of differential equations. Autom Remote Control 72, 1822–1832 (2011). https://doi.org/10.1134/S0005117911090049

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117911090049

Keywords

Search

Navigation