Geodesic
Stabilization of a nonlinear control system on the Lie group $ SO(3)\times \mathbb{R}^3\times \mathbb{R}^3 $
Petrişor, Camelia1
1 Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei, Nr. 2, 300006-Timişoara, România
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 5, p. 2019-2030.

Voir la notice de l'article provenant de la source International Scientific Research Publications

The stabilization of some equilibrium points of a dynamical system via linear controls is studied. Numerical integration using Lie-Trotter integrator and its properties are also presented.
DOI : 10.22436/jnsa.009.05.08
Classification : 34H05, 53D17
Keywords: Optimal control problem, Hamilton-Poisson system, nonlinear stability, numerical integration.

Petrişor, Camelia 1

1 Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei, Nr. 2, 300006-Timişoara, România 
@article{JNSA_2016_9_5_a7,
     author = {Petri\c{s}or, Camelia},
     title = {Stabilization of a nonlinear control system on the {Lie} group \( {SO(3)\times} {\mathbb{R}^3\times} {\mathbb{R}^3} \)},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {2019-2030},
     publisher = {mathdoc},
     volume = {9},
     number = {5},
     year = {2016},
     doi = {10.22436/jnsa.009.05.08},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.05.08/}
}
TY  - JOUR
AU  - Petrişor, Camelia
TI  - Stabilization of a nonlinear control system on the Lie group \( SO(3)\times \mathbb{R}^3\times \mathbb{R}^3 \)
JO  - Journal of nonlinear sciences and its applications
PY  - 2016
SP  - 2019
EP  - 2030
VL  - 9
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.05.08/
DO  - 10.22436/jnsa.009.05.08
LA  - en
ID  - JNSA_2016_9_5_a7
ER  - 
%0 Journal Article
%A Petrişor, Camelia
%T Stabilization of a nonlinear control system on the Lie group \( SO(3)\times \mathbb{R}^3\times \mathbb{R}^3 \)
%J Journal of nonlinear sciences and its applications
%D 2016
%P 2019-2030
%V 9
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.05.08/
%R 10.22436/jnsa.009.05.08
%G en
%F JNSA_2016_9_5_a7
Petrişor, Camelia. Stabilization of a nonlinear control system on the Lie group \( SO(3)\times \mathbb{R}^3\times \mathbb{R}^3 \). Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 5, p. 2019-2030. doi : 10.22436/jnsa.009.05.08. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.05.08/

[1] Bloch, A. M.; Krishnaprasad, P. S.; Marsden, J. E.; Alvarez, G. Sanchez de Stabilization of Rigid Body Dynamics by Internal and External Torques, Automatica J., Volume 28 (1992), pp. 745-756

[2] C. Petrişor Some New Remarks about the Dynamics of an Automobile with Two Trailers, J. Appl. Math., Volume 2014 (2014), pp. 1-6

[3] Pop, C. A Drift-Free Left Invariant Control System on the Lie Group \(SO(3)\times \mathbb{R}^3\times \mathbb{R}^3 \), Math. Probl. Eng., Volume 2015 (2015), pp. 1-9

[4] Pop, C.; Aron, A.; Petrişor, C. Geometrical aspects of the ball-plate problem, Balkan J. Geom. Appl., Volume 16 (2011), pp. 114-121

[5] C. Pop Arieşanu Stability Problems for Chua System with One Linear Control , J. Appl. Math., Volume 2013 (2013), pp. 1-5

[6] Puta, M. On the Maxwell-Bloch equations with one control, C. R. Acad. Sci. Paris, Sér. I Math., Volume 318 (1994), pp. 679-683

[7] Puta, M. On an Extension of the 3-Dimensional Toda Lattice, Differential geometry and applications (Brno, 1995), 455-462, Masaryk Univ., Brno, 1996

[8] Trotter, H. F. On the Product of Semi-Operators, Proc. Amer. Math. Soc., Volume 10 (1959), pp. 545-551

Cité par Sources :