Skip to main content
Log in

Affine Controlled Systems and t-Systems of Pfaffian Equations

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

Abstract

The relation between the classical theory of Pfaffian systems and the modern theory of controlled systems is discussed. It is shown that this relation helps solve classification problems and terminal control problems for controlled systems.

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. P. K. Rashevskii, Geometric Theory of Partial Differential Equations (Gostekhizdat, Moscow, 1947) [in Russian].

    Google Scholar 

  2. J. A. Schouten and W. van der Kulk, Pfaff’s Problem and Its Generalizations (Clarendon, Oxford, 1949).

    MATH  Google Scholar 

  3. V. I. Arnold, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Maps (Nauka, Moscow, 1982; Birkhäuser, Boston, 1985).

  4. V. I. Elkin, “Reduction of underdetermined systems of ordinary differential equations I,” Differ. Equations 45 (12), 1721–1731 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  5. V. I. Elkin, “Reduction of underdetermined systems of ordinary differential equations II,” Differ. Equations 46 (11), 1525–1536 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  6. V. I. Elkin, “Reduction of underdetermined systems of ordinary differential equations III,” Differ. Equations 47 (11), 1556–1562 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  7. V. I. Elkin, “Reduction of underdetermined systems of ordinary differential equations IV,” Differ. Equations 48 (11), 1437–1443 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  8. V. I. Elkin, “Reduction of underdetermined systems of ordinary differential equations V,” Differ. Equations 51 (1), 1–10 (2015).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. I. Elkin.

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

Elkin, V.I. Affine Controlled Systems and t-Systems of Pfaffian Equations. Comput. Math. and Math. Phys. 58, 1049–1057 (2018). https://doi.org/10.1134/S0965542518070060

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542518070060

Keywords:

Navigation