Linear control systems on the homogeneous spaces of the 2D Lie group. (English) Zbl 1483.93036
Summary: In this paper, we classify all the possible linear control systems on the homogeneous spaces of the 2D solvable Lie group and study their controllability and control sets.
MSC:
| 93B05 | Controllability |
| 93C05 | Linear systems in control theory |
| 22E25 | Nilpotent and solvable Lie groups |
References:
| [1] | Ayala, V.; Da Silva, A., Controllability of linear control systems on Lie groups with semisimple finite center, SIAM J. Control Optim., 55, 2, 1332-1343 (2017) · Zbl 1368.93030 |
| [2] | Ayala, V.; Da Silva, A., On the characterization of the controllability property for linear control systems on nonnilpotent, solvable three-dimensional Lie groups, J. Differ. Equ., 266, 12, 8233-8257 (2019) · Zbl 1409.93012 |
| [3] | Ayala, V.; Da Silva, A., The control set of a linear control system on the two dimensional Lie group, J. Differ. Equ., 268, 11, 6683-6701 (2020) · Zbl 1440.93025 |
| [4] | Ayala, V.; Da Silva, A.; Jouan, P.; Zsigmond, G., Control sets of linear systems on semi-simple Lie groups, J. Differ. Equ., 269, 5, 449-466 (2020) · Zbl 1440.93102 |
| [5] | Ayala, V.; San Martin, L. A.B., Controllability properties of a class of control systems on Lie groups, (Isidori, A.; Lamnabhi-Lagarrigue, F.; Respondek, W., Nonlinear Control in the Year 2000. Nonlinear Control in the Year 2000, Lecture Notes in Control and Information Sciences, vol. 258 (2001), Springer: Springer London) · Zbl 1239.93009 |
| [6] | Ayala, V.; Tirao, J., Linear control systems on Lie groups and controllability, (Proceedings of Symposia in Pure Mathematics, vol. 64 (1999)) · Zbl 0916.93015 |
| [7] | Colonius, F.; Kliemann, W., The Dynamics of Control (2000), Birkhäuser: Birkhäuser Boston · Zbl 0718.34091 |
| [8] | Dath, M.; Jouan, P., Controllability of linear systems on low dimensional nilpotent and solvable Lie groups, J. Dyn. Control Syst., 22, 2, 207-225 (2016) · Zbl 1333.93048 |
| [9] | Jouan, Ph., Controllability of linear systems on Lie group, J. Dyn. Control Syst., 17, 591-616 (2011) · Zbl 1236.93020 |
| [10] | Jouan, Ph., Equivalence of control systems with linear systems on Lie groups and homogeneous spaces, ESAIM Control Optim. Calc. Var., 16, 956-973 (2010) · Zbl 1210.93024 |
| [11] | Leitmann, G., Optimization Techniques with Application to Aerospace Systems (1962), Academic Press Inc.: Academic Press Inc. London · Zbl 0133.05602 |
| [12] | Markus, L., Controllability of multi-trajectories on Lie groups, (Rand, D.; Young, L. S., Dynamical Systems and Turbulence. Dynamical Systems and Turbulence, Warwick 1980. Dynamical Systems and Turbulence. Dynamical Systems and Turbulence, Warwick 1980, Lecture Notes in Mathematics, vol. 898 (1981), Springer: Springer Berlin, Heidelberg) · Zbl 0515.34054 |
| [13] | Wonham, W. M., Linear Multivariable Control: A Geometric Approach (1979), Springer-Verlag: Springer-Verlag New York · Zbl 0393.93024 |
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