SciELO - Scientific Electronic Library Online

 
vol.38 número3On a new class of generalized difference sequence spaces of fractional order defined by modulus functionA new type of generalized closed set via γ-open set in a fuzzy bitopological space índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados

Revista

Articulo

Indicadores

Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google

Compartir


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.3 Antofagasta ago. 2019

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

Articles

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

1Yildiz Technical University, Department of Mathematics, Davutpasa Campus, 34220, Istanbul, Turkey. e-mail : akhansen@ase.au.dk

2Yildiz Technical University, Department of Mathematics, Davutpasa Campus, 34220, Istanbul, Turkey. e-mail : mahmut.kudeyt@isikun.edu.tr

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.

Keywords: Controllability; Affine algebra; Automorphism; Derivation; Free nilpotent Lie group

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgement

The second author was supported by TUBITAK- The Scientific and Technological Research Council of Turkey.

References

[1] 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. [ Links ]

[2] 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/2GL8IykLinks ]

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

[4] 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. [ Links ]

[5] 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. [ Links ]

[6] 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 [ Links ]

Received: April 2018; Accepted: November 2018

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License