Controllability of affine systems on free Nilpotent Lie groups Gm,?

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2019-03-0032

Keywords:

Controllability, Affine algebra, Automorphism, Derivation, Free nilpotent lie group

Abstract

Controllability properties of affine control systems on free nilpotent Lie groups are examined and controllability of affine systems on thiskind of Lie groups are characterized by the help of their associated bilinear parts. In order to show this, an automorphism in the algebra level is found, authomosrpism orbit of the system is calculated and its properties are studied.

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Author Biographies

  • Ayse Kara Hansen, Yildiz Technical University.

    Department of Mathematics.

  • Mahmut Kudeyt, Yildiz Technical University.

    Department of Mathematics.

References

V. Jurdjevic and G. Sallet, “Controllability properties of affine systems”, SIAM Journal on Control and Optimization, vol. 22, no. 3, pp. 501–508, 1984, doi: 10.1137/0322030.

A. Kara and L. San Martin, “Controllability of affine control systems for the generalized Heisenberg lie groups”, International Journal of Pure and Applied Mathematics, vol. 29, no. 1, 2006. [On line]. Available: http://bit.ly/2GL8Iyk

V. Jurdjevic, Geometric Control Theory. Cambridge: Cambridge University Press, 1996, doi: 10.1017/CBO9780511530036.

A. Bonfiglioli, F. Uguzzoni and E. Lanconelli, Stratified Lie Groups and Potential Theory for Their Sub-Laplacians, (Springer Monographs in Mathematics), Berlin: Springer, 2008, doi: 10.1007/978-3-540-71897-0.

M. Grayson and R. Grossman, “Models for free nilpotent Lie algebras”, Journal of Algebra, vol. 135, no. 1, pp. 177–191, Nov. 1990, doi: 10.1016/0021-8693(90)90156-I.

H. Sussmann, “Some properties of vector field systems that are not altered by small perturbations”, Journal of Differential Equations, vol. 20, no. 2, pp. 292–315, Mar. 1976, doi: 10.1016/0022-0396(76)90109-1.

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Published

2019-08-14

Issue

Vol. 38 No. 3 (2019)

Section

Artículos

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How to Cite

[1]
“Controllability of affine systems on free Nilpotent Lie groups Gm,?”, Proyecciones (Antofagasta, On line), vol. 38, no. 3, pp. 499–509, Aug. 2019, doi: 10.22199/issn.0717-6279-2019-03-0032.