Victor Ayala

CONTROLLABILITY OF LINEAR SYSTEMS ON LIE GROUPS WITH FINITE SEMISIMPLE CENTER

In this paper we extend the results on controllability of linear systems obtained in Controllability of linear systems on solvable Lie groups, from solvable Lie groups to Lie groups with finite semisimple center.

Almost-Riemannian Geometry on Lie Groups

A simple Almost-Riemmanian Structure on a Lie group G is defined by a linear vector field and dim(G)-1 left-invariant ones. We state results about the singular locus, the abnormal extremals and the desingularization of such ARSs, and these results are illustrated by examples on the 2D affine and the Heisenberg groups.These ARSs are extended in two ways to homogeneous spaces, and a necessary and sufficient condition for an ARS on a manifold to be equivalent to a general ARS on a homogeneous space is stated.

Controllability on

In this paper we study controllability of affine invariant control systems on the group

\mathrm{Sl}(2,\mathbb{C})

mathrm{Sl}(2,mathbb{C})

with Restricted Controls

with restricted controls. We develop a method based on the action of

Boundedness control sets for linear systems on Lie groups

mathrm{Sl}(2,mathbb{C})

The dynamic of a Lie group endomorphism

on the sphere

On the characterization of the controllability property for linear control systems on nonnilpotent, solvable three-dimensional Lie groups

S^{2}approx mathbb{C}cup {infty}

Chaos on Set-Valued Dynamics and Control Sets

by Mobius 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 [J. Differential Equations, 39 (1981), pp. 186--211].

ALGUNOS ASPECTOS MATEMÁTICOS DE LOS SISTEMAS DE CONTROL LINEALES A TRAVÉS DE UN PROBLEMA DE OPTIMIZACIÓN

Abstract Let Σ be a linear system on a connected Lie group G and assume that the reachable set 𝓐 from the identity element e ∈ G is open. In this paper, we give an algebraic condition to warrant the boundedness of the existent control set with a nonempty interior containing e. We concentrate the search for the class of decomposable groups which includes any solvable group and also every compact semisimple group.