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Related papers: Approximately controllable finite-dimensional bili…

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Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport…

Optimization and Control · Mathematics 2019-05-17 Birgit Jacob , Julia T. Kaiser

Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…

Optimization and Control · Mathematics 2025-11-18 Manuel Rissel , Marius Tucsnak

In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…

Optimization and Control · Mathematics 2018-10-03 Xu Liu , Qi Lü , Xu Zhang

We study the controllability of the Bloch equation, for an ensemble of non interacting half-spins, in a static magnetic field, with dispersion in the Larmor frequency. This system may be seen as a prototype for infinite dimensional bilinear…

Optimization and Control · Mathematics 2015-05-13 Karine Beauchard , Jean-Michel Coron , Pierre Rouchon

Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…

Optimization and Control · Mathematics 2016-01-14 Shuo Wang , Jr-Shin Li

The aim of this paper is to provide a short introduction to modern issues in the control of infinite dimensional closed quantum systems, driven by the bilinear Schr\"odinger equation. The first part is a quick presentation of some of the…

Optimization and Control · Mathematics 2013-04-29 Ugo Boscain , Thomas Chambrion , Mario Sigalotti

We provide bounds on the error between dynamics of an infinite dimensional bilinear Schr\"odinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used on the finite dimensional approximations…

Optimization and Control · Mathematics 2015-03-19 Nabile Boussaïd , Marco Caponigro , Thomas Chambrion

This document explores structural controllability of polynomial dynamical systems or polysystems. We extend Lin's concept of structural controllability for linear systems, offering hypergraph-theoretic methods to rapidly assess strong…

Optimization and Control · Mathematics 2023-10-17 Joshua Pickard

We study the controllability of a closed control-affine quantum system driven by two or more external fields. We provide a sufficient condition for controllability in terms of existence of conical intersections between eigenvalues of the…

Mathematical Physics · Physics 2015-06-17 Ugo Boscain , Jean-Paul Gauthier , Francesco Rossi , Mario Sigalotti

Structural controllability challenges arise from imprecise system modeling and system interconnections in large scale systems. In this paper, we study structural control of bilinear systems on the special Euclidean group. We employ graph…

Optimization and Control · Mathematics 2024-06-18 A. Sanand Amita Dilip , Chirayu D. Athalye

In this paper, we consider a parabolic PDE on a torus of arbitrary dimension. The nonlinear term is a smooth function of polynomial growth of any degree. In this general setting, the corresponding Cauchy problem is not necessarily well…

Analysis of PDEs · Mathematics 2020-06-16 Vahagn Nersesyan

In this paper, we consider the bilinear approximate controllability for the complex Ginzburg-Landau (CGL) equation with a power-type nonlinearity of any integer degree on a torus of arbitrary space dimension. Under a saturation hypothesis…

Optimization and Control · Mathematics 2025-12-30 Xingwu Zeng , Can Zhang

Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spaces. In the setup, we assume only that the drift and control…

Optimization and Control · Mathematics 2026-05-14 Dimitrios Giannakis , Gage Hoefer

We show that we can achieve global density-operator controllability for most N-dimensional bilinear Hamiltonian control systems with general fixed couplings using a single, locally-acting actuator that modulates one energy-level transition.…

Quantum Physics · Physics 2009-11-13 Sonia G. Schirmer , Ivan C. H. Pullen , Peter J. Pemberton-Ross

In this work we extend a variational method to study the approximate controllability and finite dimensional exact controllability ( finite-approximate controllability) for the semilinear evolution equations in Hilbert spaces. We state a…

Analysis of PDEs · Mathematics 2018-06-20 N. I. Mahmudov

We consider a linear Schr\"odinger equation, on a bounded interval, with bilinear control. Beauchard and Laurent proved that, under an appropriate non degeneracy assumption, this system is controllable, locally around the ground state, in…

Optimization and Control · Mathematics 2013-01-17 Karine Beauchard , Morgan Morancey

An algebraic characterization of the property of approximate controllability is given, for behaviours of spatially invariant dynamical systems, consisting of distributional solutions, that are periodic in the spatial variables, to a system…

Optimization and Control · Mathematics 2014-02-19 Amol Sasane

We consider a non-resonant system of finitely many bilinear Schroedinger equations with discrete spectrum driven by the same scalar control. We prove that this system can approximately track any given system of trajectories of density…

Optimization and Control · Mathematics 2009-02-24 Thomas Chambrion

We consider a linear Schr\"odinger equation, on a bounded interval, with bilinear control, that represents a quantum particle in an electric field (the control). We prove the controllability of this system, in any positive time, locally…

Analysis of PDEs · Mathematics 2010-01-20 Karine Beauchard , Camille Laurent

The aim of this work is to study the controllability of the bilinear Schr\"odinger equation on compact graphs. In particular, we consider the equation (BSE) $i\partial_t\psi=-\Delta\psi+u(t)B\psi$ in the Hilbert space…

Mathematical Physics · Physics 2020-07-17 Alessandro Duca