The General Solution for Affine Control Systems on Lie Groups

Control Affine Systems on Solvable Three-dimensional Lie Groups, I

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.

Control Systems on Lie Groups

Controllability of Affine Systems for the Generalized Heisenberg Lie Groups

Affine control systems on the generalized Heisenberg Lie groups are studied. Controllability of this kind of class of systems on the generalized Heisenberg Lie group is established by relating to their associated bilinear part. AMS Subject Classification: 22E20

Controllability of affine right-invariant systems on solvable Lie groups

First we recall definitions and state our problem. Let G be a real connected Lie group, L be its Lie algebra (i.e. the set of all right-invariant vector fields on G). For any A;B1; : : : ; Bm 2 L we consider the corresponding affine right-invariant system = fA+ m Xi=1 uiBi j 8i ui 2 Rg The attainable set A for the system is a subsemigroup of G generated by one-parameter semigroups f exp(tX) j X...

Affine structures on abelian Lie Groups

The Nagano-Yagi-Goldmann theorem states that on the torus T, every affine (or projective) structure is invariant or is constructed on the basis of some Goldmann rings [N-Y]. It shows the interest to study the invariant affine structure on the torus T or on abelian Lie groups. Recently, the works of Kim [K] and Dekempe-Ongenae [D-O] precise the number of non equivalent invariant affine structure...