Skip to main content
SpringerLink
Log in

Application of Differential-Geometric Methods of Control Theory to the Theory of Partial Differential Equations. I

  • CONTROL THEORY
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We consider the application of differential-geometric and algebraic methods of the theory of dynamical control systems to the theory of partial differential equations.

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. Yakovenko, G.N., Teoriya upravleniya regulyarnymi sistemami (Control Theory of Regular Systems), Moscow: Binom. Lab. Znanii, 2008.

    Google Scholar 

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

    MATH  Google Scholar 

  3. Elkin, V.I., Reduktsiya nelineinykh upravlyaemykh sistem. Dekompozitsiya i invariantnost’ po vozmushcheniyam (Reduction of Nonlinear Control Systems. Decomposition and Perturbation Invariance), Moscow: FAZIS, 2003.

    Google Scholar 

  4. Elkin, V.I., Reduktsiya nelineinykh upravlyaemykh sistem. Simmetrii i klassifikatsiya (Reduction of Nonlinear Control Systems. Symmetries and Classification), Moscow: FAZIS, 2006.

    Google Scholar 

  5. Chebotarev, N.G., Nepreryvnye gruppy preobrazovanii (Continuous Groups of Transformations), Moscow–Leningrad, 1940.

  6. Eisenhart, L.P., Continuous Groups of Transformations, 1933. Translated under the title: Nepreryvnye gruppy preobrazovanii, Moscow: Gos. Izd. Inostr. Lit., 1947.

  7. Hermann, R. and Krener, A.J., Nonlinear controllability and observability, IEEE Trans. Autom. Control, 1977, vol. AC–22, no. 5, pp. 728–740.

    Article  MathSciNet  Google Scholar 

  8. Olver, P., Applications of Lie Groups to Differential Equations, New York–Berlin–Heidelberg–Tokyo: Springer-Verlag, 1986. Translated under the title: Prilozheniya grupp Li k differentsial’nym uravneniyam, Moscow: Mir, 1989.

    Book  Google Scholar 

  9. Rashevskii, P.K., Geometricheskaya teoriya uravnenii s chastnymi proizvodnymi (Geometric Theory of Partial Differential Equations), Moscow–Leningrad: OGIZ, 1947.

    Google Scholar 

  10. Lur’e, K.A., Optimal’noe upravlenie v zadachakh matematicheskoi fiziki (Optimal Control in Problems of Mathematical Physics), Moscow: Nauka, 1975.

    Google Scholar 

  11. Bocharov, A.V., Verbovetskii, A.M., Vinogradov, A.M., et al., Simmetrii i zakony sokhraneniya uravnenii matematicheskoi fiziki (Symmetries and Conservation Laws for Equations of Mathematical Physics), Moscow: Faktorial Press, 2005.

    Google Scholar 

Download references

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00625.

Author information

Authors and Affiliations

  1. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

    V. I. Elkin

Authors
  1. V. I. Elkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Elkin.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Elkin, V.I. Application of Differential-Geometric Methods of Control Theory to the Theory of Partial Differential Equations. I. Diff Equat 57, 1451–1459 (2021). https://doi.org/10.1134/S0012266121110057

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266121110057

Search

Navigation