Related papers: A necessary and sufficient condition for local con…
In this note we prove a necessary set of conditions which must be satisfied by any controlled gate in the qubit Clifford Hierarchy. These conditions are straightforward to derive yet quite restricting. We also extend our proofs to gates…
We prove that there exists at least one close orbit in a given contact hypersurface in some symplectic manifolds.
We prove that for a weakly exact magnetic system on a closed connected Riemannian manifold, almost all energy levels contain a closed orbit. More precisely, we prove the following stronger statements. Let $(M,g)$ denote a closed connected…
In this article, we give a condition for the global controllability of affine nonlinear control systems with drifts on Euclidean spaces. Under regularity assumptions, the condition is necessary and sufficient in the codimension-1 and…
In this paper, we propose new conditions guaranteeing that the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control…
We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…
This paper develops a new approach to small time local attainability of smooth manifolds of any dimension, possibly with boundary and to prove H\"older continuity of the minimum time function. We give explicit pointwise conditions of any…
Given a control system on a manifold that is embedded in Euclidean space, it is sometimes convenient to use a single global coordinate system in the ambient Euclidean space for controller design rather than to use multiple local charts on…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
This paper is devoted to prove the exact controllability of a system of N one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We consider the case where the coupling matrix A…
This paper presents a closed-form notion of controllability and observability for systems with communication delays, actuation delays, and locality constraints. The formulation reduces to classical notions of controllability and…
Sufficient conditions for the controllability of a conservative reduced system are given. Several examples illustrating the theory are also presented.
This note deals with the local exact controllability to a particular class of trajectories for the Boussinesq system with nonlinear Navier-slip boundary conditions and internal controls having vanishing components. Briefly speaking, in two…
This paper is devoted to prove the local exact controllability to the trajectories for a coupled system, of the Boussinesq kind, with a reduced number of controls. In the state system, the unknowns are the velocity field and pressure of the…
We obtain a sufficient condition, given a totally disconnected, locally compact group $G$ with a topologically simple monolith $S$, to ensure that $S$ is open in $G$ and abstractly simple.
We examine bound orbits of particles around singly rotating black rings. We show that there exist stable bound orbits in toroidal spiral shape near the axis of the ring, and also exist stable circular orbits on the axis as special cases.…
In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…
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 work, we consider the problem of event-triggered implementation of control laws designed for the local stabilization of nonlinear systems with center manifolds. We propose event-triggering conditions which are derived from a local…
This article presents a path-following control law for autonomous orbital maintenance of small body missions. The control law is robust, stable, and capable of controlling only the orbital geometry, allowing the spacecraft to operate with…