Skip to main content
SpringerLink
Log in

Controllability of hypersurface and solvable invariant systems

  • Published:
Journal of Dynamical and Control Systems Aims and scope Submit manuscript

Abstract

This paper deals with affine invariant control systems on Lie groups. Controllability conditions for hypersurface systems and for systems on solvable simply connected Lie groups are obtained. A lower bound of the number of controlled vector fields necessary to achieve controllability on simply connected Lie groups is given.

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. V. Jurdjevic and H. Sussmann, Control systems on Lie groups.J. Differ. Equ. 12 (1972), 313–329.

    Article  Google Scholar 

  2. V. Jurdjevic and I. Kupka, Control systems on semi-simple Lie groups and their homogeneous spaces.Ann. Inst. Fourier, Grenoble 31 (1981), No. 4, 151–179.

    Google Scholar 

  3. J.-P. Gauthier and G. Bornard, Contrôlabilité des systèmes bilinèaires.SIAM J. Control Optim. 20 (1982), No. 3, 377–384.

    Article  Google Scholar 

  4. F. Silva Leite and P. C. Crouch, Controllability on classical Lie groups,Math. Control Signals Syst. 1 (1988), 31–42.

    Google Scholar 

  5. R. El Assoudi and J.-P. Gauthier, Controllability of right-invariant systems on semi-simple Lie groups.New Trends in Nonlinear Control Theory, Springer-Verlag 122 (1989), 54–64.

    Google Scholar 

  6. V. A. Bravo and L. S. Martin, Controllability of nilpotent systems.Preprint IC/93/30.UNESCO Intern. Centre for Theor. Physics, Trieste, Italy, 1993.

  7. M. Lovric, Left-invariant control systems on Lie groups.Preprint F193-CT03.The Fields Institute for Research in Mathematical Sciences, Canada, January 1993.

    Google Scholar 

  8. V. Ayala and J. Tirao, Controllability of linear vector fields on Lie groups.Preprint IC/94/310.UNESCO Intern. Centre for Theor. Physics.Trieste, Italy, 1994.

    Google Scholar 

  9. M. J. Enos, Controllability of a system of two symmetric rigid bodies in three space.SIAM J. Control Optim. 32 (1994), No. 4.

    Google Scholar 

  10. Y. L. Sachkov, Controllability of invariant systems on Lie groups: hypersurface approach.Preprint No. IT-95-276. LIFL,University Lille I, France, April 1995.

    Google Scholar 

  11. —, Controllability of invariant systems on solvable Lie groups,Preprint No. IT-95-281. LIFL,University Lille I, France, May 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Program Systems Institute, 152140, Pereslavl-Zalessky, Russia

    Yu. L. Sachkov

Authors
  1. Yu. L. Sachkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was written when the author was visiting Laboratoire d'Informatique Fondamentale de Lille, Université Lille I, France.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sachkov, Y.L. Controllability of hypersurface and solvable invariant systems. Journal of Dynamical and Control Systems 2, 55–67 (1996). https://doi.org/10.1007/BF02259622

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02259622

1991 Mathematics Subject Classification

Key words and phrases

Search

Navigation