Control affine systems on solvable three-dimensional Lie groups, I

Rory Biggs; Claudiu C. Remsing

Archivum Mathematicum (2013)

  • Volume: 049, Issue: 3, page 187-197
  • ISSN: 0044-8753

Abstract

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We seek to classify the full-rank left-invariant control affine systems evolving on solvable three-dimensional Lie groups. In this paper we consider only the cases corresponding to the solvable Lie algebras of types II, IV, and V in the Bianchi-Behr classification.

How to cite

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Biggs, Rory, and Remsing, Claudiu C.. "Control affine systems on solvable three-dimensional Lie groups, I." Archivum Mathematicum 049.3 (2013): 187-197. <http://eudml.org/doc/260595>.

@article{Biggs2013,
abstract = {We seek to classify the full-rank left-invariant control affine systems evolving on solvable three-dimensional Lie groups. In this paper we consider only the cases corresponding to the solvable Lie algebras of types II, IV, and V in the Bianchi-Behr classification.},
author = {Biggs, Rory, Remsing, Claudiu C.},
journal = {Archivum Mathematicum},
keywords = {left-invariant control system; (detached) feedback equivalence; affine subspace; solvable Lie algebra; left-invariant control system; (detached) feedback equivalence; affine subspace; solvable Lie algebra},
language = {eng},
number = {3},
pages = {187-197},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Control affine systems on solvable three-dimensional Lie groups, I},
url = {http://eudml.org/doc/260595},
volume = {049},
year = {2013},
}

TY - JOUR
AU - Biggs, Rory
AU - Remsing, Claudiu C.
TI - Control affine systems on solvable three-dimensional Lie groups, I
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 3
SP - 187
EP - 197
AB - We seek to classify the full-rank left-invariant control affine systems evolving on solvable three-dimensional Lie groups. In this paper we consider only the cases corresponding to the solvable Lie algebras of types II, IV, and V in the Bianchi-Behr classification.
LA - eng
KW - left-invariant control system; (detached) feedback equivalence; affine subspace; solvable Lie algebra; left-invariant control system; (detached) feedback equivalence; affine subspace; solvable Lie algebra
UR - http://eudml.org/doc/260595
ER -

References

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  2. Biggs, R., Remsing, C. C., On the equivalence of control systems on Lie groups, submitted. 
  3. Biggs, R., Remsing, C. C., A category of control systems, An. Ştiinţ. Univ. Ovidius Constanţa Ser. Mat. 20 (1) (2012), 355–368. (2012) Zbl1274.93062MR2928428
  4. Biggs, R., Remsing, C. C., A note on the affine subspaces of three–dimensional Lie algebras, Bul. Acad. Ştiinţe Repub. Mold. Mat. no. 3 (2012), 45–52. (2012) MR3155842
  5. Biggs, R., Remsing, C. C., Control affine systems on semisimple three–dimensional Lie groups, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) 59 (2) (2013), 399–414. (2013) 
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  10. Jurdjevic, V., Geometric Control Theory, Cambridge University Press, 1977. (1977) MR1425878
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  14. MacCallum, M. A. H., On the Classification of the Real Four–Dimensional Lie Algebras, On Einstein's Path: Essays in Honour of E. Schücking (Harvey, A., ed.), Springer Verlag, 1999, pp. 299–317. (1999) Zbl0959.17003MR1658911
  15. Popovych, R. O., Boyco, V. M., Nesterenko, M. O., Lutfullin, M. W., 10.1088/0305-4470/36/26/309, J. Phys. A: Math. Gen. 36 (2003), 7337–7360. (2003) MR2004893DOI10.1088/0305-4470/36/26/309
  16. Remsing, C. C., Optimal control and Hamilton–Poisson formalism, Int. J. Pure Appl. Math. 59 (1) (2001), 11–17. (2001) MR2642777

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