Skip to main content
SpringerLink
Log in

Solution of a control problem for a nilpotent system

  • Short Communications
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We consider a control problem for systems described by ordinary differential equations with linear controls. The solution of the control problem for a three-dimensional nilpotent system with two-dimensional control is presented in the classes of trigonometric controls, piecewise constant controls, and controls minimizing the sub-Riemannian length functional. The corresponding programmed controls and synthesis families are constructed.

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

References

  1. Agrachev, A.A. and Sarychev, A.V., Dokl. Akad. Nauk SSSR, 1987, vol. 295, pp. 777–781.

    Google Scholar 

  2. Hermes, H., SIAM J. Control Optim., 1986, vol. 24, pp. 731–736.

    Article  MATH  MathSciNet  Google Scholar 

  3. Bellaiche, A., in Sub-Riemannian Geometry, Bellaiche, A. and Risler, J.-J., Eds., Basel: Birkhäuser, 1996, pp. 1–78.

    Google Scholar 

  4. Laferriere, G. and Sussmann, H.J., in Nonholonomic Motion Planning, Li Zexiang and Canny, J.F., Eds., The Kluwer International Series in Engineering and Computer Science, 1992, vol. 192.

  5. Sachkov, Yu.L. and Sachkova, E.F., in Generalized Solutions in Control Problems (IFAC workshop), Moscow, 2004, pp. 227–235.

  6. Vershik, A.M. and Gershkovich, V.Ya., Itogi Nauki Tekh. Ser. Sovrem. Probl. Mat. Fundament. Napr. Dinam. Sist., 1986, vols. 7, 8.

  7. Agrachev, A.A. and Sachkov, Yu.L., Geometricheskaya teoriya upravleniya (Control Theory from the Geometric Viewpoint), Moscow: Fizmatlit, 2005.

    Google Scholar 

  8. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Fizmatgiz, 1969.

    Google Scholar 

  9. Laumond, J.P., Lecture Notes in Control and Inform. Sci., vol. 229, Springer, 1998, p. 343.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, 152020, Russia

    E. F. Sachkova

Authors
  1. E. F. Sachkova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © E.F. Sachkova, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 12, pp. 1704–1707.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sachkova, E.F. Solution of a control problem for a nilpotent system. Diff Equat 44, 1768–1772 (2008). https://doi.org/10.1134/S0012266108120148

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266108120148

Keywords

Search

Navigation