Controllability of affine systems on free Nilpotent Lie groups Gm,?
DOI:
https://doi.org/10.22199/issn.0717-6279-2019-03-0032Keywords:
Controllability, Affine algebra, Automorphism, Derivation, Free nilpotent lie groupAbstract
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.
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.
Published
How to Cite
Issue
Section
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
