A note on the linear control systems for homogeneous spaces of the Heisenberg group

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Duman O., Kızıl E., Da Silva A.

CONGRESO DE MATEMÁTICA CAPRICORNIO (COMCA), Iquique, Şili, 3 - 05 Ağustos 2022, ss.68

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Iquique
  • Basıldığı Ülke: Şili
  • Sayfa Sayıları: ss.68
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

A control system on a connected Lie group 

\begin{equation}\label{control}

\dot{q(t)} = \mathcal{X}_{q(t)}+\sum_{i=1}^{n} u_i(t) Y_{q(t)}^{i}=f (q(t),u(t))

\end{equation}

is called to be linear if drift vector field $\mathcal{X}$ is linear and $Y^{i}$'s are right invariant vector fields. Proved in \cite{Jouan} that any control-affine system on a connected manifold, whose associated vector fields are complete and generate a finite Lie algebra is diffeomorphic to a LCS on a homogeneous space. The significance of this result is that it extend LCS to homogeneous spaces. Therefore, the question of how the concept of controllability and control sets differ in the space and its homogeneous spaces has gained importance. Here we investigate the controllability property and the control sets of (\ref{control}) on a homogeneous space of the Heisenberg Lie group.


Joint work with:  

Adriano Da Silva, adasilva@academicos.uta.cl, Departamento de Matematica, Universidad de Tarapaca, Arica, Chile.

Eyup Kizil, kizil@yildiz.edu.tr, Department of Mathematics, Yildiz Technical University, Istanbul, Turkey.