相关论文: Attainable sets for left invariant control systems…

Using the semigroup approach to abstract boundary control problems we characterize the space of all exactly reachable states. Moreover, we study the situation when the controls of the system are required to be positive. The abstract results…

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…

In this work, we study controllability in the set of all density matrices for a two-level open quantum system driven by coherent and incoherent controls. In [A. Pechen, Phys. Rev. A 84, 042106 (2011)] an approximate controllability, i.e.,…

A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for $6$-dimensional nilmanifolds whose…

In this paper, we obtain weak conditions for the existence of a control set with a nonempty interior for a linear control system on a solvable Lie group. We show that the Lie algebra rank condition together with the compactness of the…

In this paper, we prove results concerning the large scale geometry of connected, simply connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics. Precisely, we prove that there do not exist quasi-isometric…

We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…

We give a necessary and sufficient condition for a set of left invariant metrics on a compact Heisenberg manifold to be relatively compact in the corresponding moduli space.

This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift…

The present paper shows that the bounded control set of a linear system on a connected Lie group $G$ contains all the bounded orbits of the system. As a consequence, its closure is the continuous image of the cartesian product of the set of…

In this paper we describe the Lie-theoretic structure of ${\rm SO}(1,4)$ and consider control systems given by certain vector fields of ${\rm SO}(1,4)$. Then we explicitly describe its invariant control sets in the unique ${\rm…

The design of an invariant tracking control law for the kinematic car driving on a sphere is discussed. Using a Lie group framework a left-invariant description on SO(3) is derived. Basic geometric considerations allow a direct comparison…

In this paper, we efficiently compute overapproximating reachable sets for control systems evolving on Lie groups, building off results from monotone systems theory and geometric integration theory. We consider intervals in the tangent…

Left invariant affine structures in a Lie group $G$ are in one-to-one correspondence with left-symmetric algebras over its Lie algebra $\mathfrak g=T_eG$ (``over'' means that the commutator $[x,y]=xy-yx$ coincides with the Lie bracket;…

In the context of a connected, simply connected, nilpotent Lie group, whose representations are square-integrable modulo the center, we find characterization results of extra-invariant spaces under the left translations associated with the…

We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…

In this paper, we show that for a linear control system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as the set of singularities of the drift…

In this paper, we investigate nilpotent and unimodular solvable Lie groups that admit quasi-Einstein metrics $(M,g,X)$ with $X$ a left-invariant vector field, which we call totally left-invariant quasi-Einstein metrics. We give a complete…

The new concept of relative generic subsets is introduced. It is shown that the set of controllable linear finite-dimensional port-Hamiltonian systems is a relative generic subset of the set of all linear finite-dimensional port-Hamiltonian…

We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of…