Artículos de revistas
Controllability On Sl(2, ℂ) With Restricted Controls
Registro en:
Siam Journal On Control And Optimization. Society For Industrial And Applied Mathematics Publications, v. 52, n. 4, p. 2548 - 2567, 2014.
3630129
10.1137/130943662
2-s2.0-84906818865
Autor
Ayala V.
Ribeiro R.
Martin L.A.B.S.
Institución
Resumen
In this paper we study controllability of affine invariant control systems on the group Sl(2, C) with restricted controls. We develop a method based on the action of Sl(2, ℂ) on the sphere S2 ≈ ℂ ∪ {∞} by Möbius functions. Some controllability results are proved. It is proved also that controllability with restricted controls is not a generic property, contrary to the case of unrestricted controls, as proved in the classic paper by Jurdjevic and Kupka. © 2014 Society for Industrial and Applied Mathematics. 52 4 2548 2567 Ayala, V., San Martin, L.A.B., Controllability of two-dimensional bilinear systems: Restricted controls and discrete-time (1999) Proyecciones, 18, pp. 207-223 El Assoudi, R., Gauthier, J.P., Kupka, I., On subsemigroups of semisimple Lie groups (1996) Ann. Inst. H. Poincaré, 13, pp. 117-133 El Assoudi, R., Semigroups of simple Lie groups and controllability (2014) J. Dyn. Control Syst., 20, pp. 91-104 Barros, C.J.B., Gonçalves, J.R., Do Rocio, O., San Martin, L.A.B., Controllability of two-dimensional bilinear systems (1996) Rev. Proyecciones, 15, pp. 111-139 Barros, C.J.B., San Martin, L.A.B., Controllability of discrete-time control systems on the symplectic group (2001) Systems Control Lett., 42, pp. 95-100 Gauthier, J.P., Kupka, I., Sallet, G., Controllability of right invariant systems on real simple Lie groups (1984) Systems Control Lett., 5, pp. 187-190 Helgason, S., (1978) Differential Geometry, in Lie Groups and Symmetric Spaces, , Academic Press, New York Jòo, I., Tuan, N.M., On controllability of bilinear systems II (controllability in two dimensions) (1992) Ann. Univ. Sci. Budapest, 35, pp. 217-265 Jurdjevic, V., Kupka, I., Control systems subordinated to a group action: Accessibility (1981) J. Differential Equations, 39, pp. 186-211 Jurdjevic, V., Kupka, I., Control systems on semisimple Lie groups and their homogeneous spaces (1981) Ann. Inst. Fourier (Grenoble), 31, pp. 151-179 Mittenhuber, D., The classification of global Lie wedges in sl (2) (1995) Manuscripta Math., 88, pp. 479-495 San Martin, L.A.B., Invariant control sets on flag manifolds (1993) Math. Control Signals Systems, 6, pp. 41-61 San Martin, L.A.B., Control sets and semigroups in semi-simple Lie groups (1995) Semigroups in Algebra, Analysis and Geometry, de Gruyter Exp. Math., pp. 275-291. , 20 Walter de Gruyter, Berlin San Martin, L.A.B., On global controllability of discrete-time control systems (1995) Math. Control Signals Systems, 8, pp. 279-297 San Martin, L.A.B., Homogeneous spaces admitting transitive semigroups (1998) J. Lie Theory, 8, pp. 111-128 San Martin, L.A.B., Tonelli, P.A., Semigroup actions on homogeneous spaces (1995) Semigroup Forum, 50, pp. 59-88 Santos, A.L., San Martin, L.A.B., Controllability of control systems on complex simple Lie groups and the topology of flag manifolds (2013) J. Dyn. Control Syst., 19, pp. 157-171