Related papers: Semigroups and Controllability of Invariant Contro…

Let $S$ be subsemigroup with nonempty interior of a complex simple Lie group $G$. It is proved that $S=G$ if $S$ contains a subgroup $G(\alpha) \approx \mathrm{Sl}(2,\mathbb{C}) $ generated by the $\exp \mathfrak{g}_{\pm \alpha}$, where…

Let $G$ be a 1-connected, almost-simple Lie group over a local field and $\mathcal{S}$ a subsemigroup of $G$ with non-empty interior. The action of the regular hyperbolic elements in the interior of $\mathcal{S}$ on the flag manifold $G/P$…

Let $G$ be a semidirect product of a simply connected nilpotent Lie group and $\R$. For a left invariant control system on $G$ with a convex cone as a control domain, it is proved that the attainable sets coincides with a "halfspace" if the…

In this paper, we investigate the controllability of bilinear control systems of the form $\dot{s} = As + uBs$, where $s \in \mathbb{S}^2$ and $A, B \in gl(3, \mathbb{R})$ are skew-symmetric matrices. First, we prove that the algebraic…

In this paper we present necessary and sufficient conditions to guarantee the existence of invariant cones, for semigroup actions, in the space of the $k$-fold exterior product. As consequence we establish a necessary and sufficient…

In this paper we study the main properties of control sets with nonempty interior of linear control systems on semisimple Lie groups. We show that, unlike the solvable case, linear control systems on semisimple Lie groups may have more than…

This paper examines the controllability for quantum control systems with SU(1,1) dynamical symmetry, namely, the ability to use some electromagnetic field to redirect the quantum system toward a desired evolution. The problem is formalized…

We describe a framework for the controllability analysis of networks of $n$ quantum systems of an arbitrary dimension $d$, {\it qudits}, with dynamics determined by Hamiltonians that are invariant under the permutation group $S_n$. Because…

Problems involving control of large ensmebles of structurally identical dynamical systems, called \emph{ensemble control}, arise in numerous scientific areas from quantum control and robotics to brain medicine. In many of such applications,…

Let us consider a linear control system \Sigma on a connected Lie group G. It is known that the accessibility set A from the identity e is in general not a semigroup. In this article we associate a new algebraic object S to \Sigma which…

In this article, we completely describe the control sets of one-input linear control systems on solvable, nonnilpotent 3D Lie groups. We show that, if the restriction of the associate derivation to the nilradical is nontrivial, the Lie…

We give necessary and sufficient conditions for the controllability of a Schr\''odinger equation involving the sub-Laplacian of a nilmanifold obtained by taking the quotient of a group of Heisenberg type by one of its discrete…

We find a necessary condition for the existence of an action of a Lie group $G$ by quaternionic automorphisms on an integrable quaternionic manifold in terms of representations of $\mathfrak{g}$. We check this condition and prove that a…

In this paper we study affine and bilinear systems on Lie groups. We show that there is an intrinsic connection between the solutions of both systems. Such relation allows us to obtain some preliminary controllability results of affne…

We describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group G. The problem reduces to the description of admissible pairs (\gk, \omega), where \gk is an appropriate regular subalgebra of…

In this paper we study the action of semigroups with nonempty interior of noncompact connected semisimple Lie groups, with finite center, on their maximal compact connected subgroups. As main results we describe the set of transitivity of a…

We study quantum systems with even numbers N of levels that are completely state-controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than the respective…

In this paper we stated a condition for the controllability of discrete-time linear systems for the case when the Lie group has finite semisimple center and provided a example in the Lie group $SL_2(\mathbb{R})$.

A time inhomogeneous generalized Mehler semigroup on a real separable Hilbert space ${\mathds{H}}$ is defined through $$ p_{s,t}f(x)=\int_{\mathds{H}} f(U(t,s)x+y)\,\mu_{t,s}(dy), \quad t\geq s, \ x\in{\mathds{H}} $$ for every bounded…

For a symmetric Lie algebra $\mathfrak g=\mathfrak k\oplus\mathfrak p$ we consider a class of bilinear or more general control-affine systems on $\mathfrak p$ defined by a drift vector field $X$ and control vector fields $\mathrm{ad}_{k_i}$…