AFFINE SINGULAR 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

Singular extremals on Lie groups

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...