Article
Mathematics, Interdisciplinary Applications
Lingfei Li, Hang Gao
Summary: This paper investigates the nonnegative approximate controllability for the one-dimensional degenerate heat equation governed by bilinear control, showing that the system is uncontrollable when the control is restricted to a fixed domain but approximately controllable when the control is allowed to move.
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
(2021)
Article
Physics, Mathematical
Ivan Beschastnyi, Ugo Boscain, Mario Sigalotti
Summary: This article discusses the preserved controllability properties of classical Hamiltonian systems after quantization and explores small-time controllability of both classical and quantum systems using the WKB method. The conjecture that lack of small-time controllability in classical systems implies the same for quantum systems is also investigated.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Automation & Control Systems
Alessandro Duca
Summary: The study focuses on the bilinear Schrodinger equation on a bounded one-dimensional domain, providing explicit times for global exact controllability and demonstrating methods for constructing controls for global approximate controllability.
INTERNATIONAL JOURNAL OF CONTROL
(2021)
Article
Mathematics, Applied
Mohamed Ouzahra
Summary: This paper focuses on the approximate controllability of a multi-dimensional semilinear reaction-diffusion equation governed by a multiplicative control. The sufficient conditions for approximately reaching the desirable state within a small time interval are provided based on linear semigroup theory and results on uniform approximation with smooth functions.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Mathematics, Applied
Fei Wang, Jun-Min Wang, Xiao-Hui Wu
Summary: This paper investigates the exact controllability of a Schrodinger equation by boundary coupling a wave equation and designing a control in the wave equation. By spectral analysis, an asymptotic expansion for the eigenvalues and eigenfunctions of the corresponding dual system is presented, and the observability inequality is obtained. The exact controllability of the coupled system is achieved based on the duality principle.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Jonas Lampart
Summary: We discuss the set of wavefunctions that can be obtained by applying the flow of the Schrodinger operator and varying the potential. We show that this set has empty interior as a subset of the L-2 (R-d) sphere and as a set of trajectories.
EVOLUTION EQUATIONS AND CONTROL THEORY
(2021)
Article
Automation & Control Systems
Alessandro Duca
Summary: The paper focuses on the dynamics of a particle trapped in networks of electrical wires or electromagnetic wave-guides under the influence of an external electromagnetic field, studying the controllability of motion and extending existing theory for bilinear quantum systems to graphs. Mathematical assumptions on the network and potential field are determined to ensure global exact controllability in suitable spaces, with practical implications discussed for specific problems involving star-shaped networks and tadpole graphs.
Article
Automation & Control Systems
M. Ouzahra
Summary: This paper investigates the control properties of the multidimensional heat equation driven by a bilinear control, including finite-time stability, null controllability, global and partial approximate controllability, and exact controllability. The approaches are based on linear semigroup theory and the controllability of the heat equation, with the use of the classical maximum principle as an essential tool.
EUROPEAN JOURNAL OF CONTROL
(2021)
Article
Automation & Control Systems
Kais Ammari, Alessandro Duca
Summary: This work examines the bilinear Schrodinger equation in the Hilbert space with an infinite graph, focusing on the Laplacian with self-adjoint boundary conditions and a bounded symmetric operator. Despite the dispersive behavior of the equation, the study explores the well-posedness of the (BSE) in suitable subspaces preserved by the dynamics, as well as global exact controllability and 'energetic controllability'. The examples provided include scenarios involving infinite tadpole graphs.
INTERNATIONAL JOURNAL OF CONTROL
(2021)
Article
Physics, Mathematical
Alberto Enciso, Daniel Peralta-Salas
Summary: This study demonstrates the existence of smooth solutions to the Gross-Pitaevskii equation on R-3, capable of describing arbitrarily complex quantum vortex reconnections and verified by experiments and numerics. Operating the Gross-Pitaevskii equation in an almost linear regime, the results are applicable to a wide range of nonlinear Schrodinger equations.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Mathematics
Jean-Michel Coron, Shengquan Xiang, Ping Zhang
Summary: In this paper, we study the global approximate controllability in small time of the quantum density and quantum momentum of the 1-D semiclassical cubic Schrodinger equation with two controls between two states with positive quantum densities. We first control the asymptotic expansions of the zeroth and first order of the physical observables via the Agrachev-Sarychev method. Then we conclude the proof through techniques of semiclassical approximation of the nonlinear Schrodinger equation.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
H. Najib, R. El Ayadi, Y. Ouakrim, M. Ouzahra
Summary: This paper investigates the exact controllability of a semilinear reaction-diffusion equation governed by a multiplicative control. The reaction term in this equation leads to an unbounded control operator. The well-posedness is studied first, followed by the question of exact steering for the system. The obtained results are further analyzed through a numerical example.
APPLICABLE ANALYSIS
(2023)
Article
Automation & Control Systems
Thomas Chambrion, Eugenio Pozzoli
Summary: In this paper, a small-time controllability property of nonlinear Schrodinger equations is proved on a d-dimensional torus T-d. The research then focuses on the linear setting, starting from a closed Riemannian manifold. The study concludes by demonstrating approximate controllability in arbitrarily small times among particular eigenfunctions of the Laplacian of the 2-dimensional sphere S-2.
Article
Automation & Control Systems
Abderrahman Ait Aadi, El Hassan Zerrik
Summary: This paper investigates a regional optimal control problem for a plate equation described by a bilinear system, in which the control is distributed, bounded, and acts on the velocity term. The study aims to prove the existence of a control solution for this problem and characterize it as a solution to an optimality system. Numerical approach is used and successfully validated through simulations.
INTERNATIONAL JOURNAL OF CONTROL
(2022)
Article
Mathematics, Applied
Brigitte E. Breckner, Hannelore Lisei, Gheorghe Ionut Simon
Summary: This study focuses on optimal solutions of nonconvex control problems associated with a class of stochastic Schrodinger type equations, exploring the existence of epsilon-optimal solutions through finite dimensional approximations and a linearization method.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Automation & Control Systems
Thomas Chambrion, Laetitia Giraldi, Alexandre Munnier
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2019)
Article
Automation & Control Systems
Thomas Chambrion, Laetitia Giraldi, Alexandre Munnier
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2019)
Article
Automation & Control Systems
Marco Caponigro, Roberta Ghezzi, Benedetto Piccoli, Emmanuel Trelat
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2018)
Article
Automation & Control Systems
Marco Caponigro, Mario Sigalotti
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2018)
Article
Mathematics
Nabile Boussaid, Marco Caponigro, Thomas Chambrion
JOURNAL OF FUNCTIONAL ANALYSIS
(2020)
Article
Mathematics, Applied
Thomas Chambrion, Laurent Thomann
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
(2020)
Article
Radiology, Nuclear Medicine & Medical Imaging
L. Van Damme, F. Mauconduit, T. Chambrion, N. Boulant, V. Gras
Summary: Parameterization-free universal nonselective pTX-pulses were successfully computed using the Gradient Ascent Pulse Engineering (GRAPE) algorithm, showing substantial improvement in excitation, refocusing, and inversion quality at off-resonance compared to kT-points and SPINS. GRAPE also allowed for a substantial reduction of pulse duration for certain imaging protocols, while maintaining similar overall performance. Performance gains were validated numerically and experimentally, but the computational burden of GRAPE currently limits its use to applications without time constraints.
MAGNETIC RESONANCE IN MEDICINE
(2021)
Article
Automation & Control Systems
Thomas Chambrion, Eugenio Pozzoli
Summary: In this study, we investigated the Schrodinger partial differential equation of a rotating symmetric rigid molecule driven by an electric field. By classifying its approximate controllability and performing numerical simulations, we achieved an orientational selective transfer of rotational population.
IEEE CONTROL SYSTEMS LETTERS
(2022)
Proceedings Paper
Automation & Control Systems
Nabile Boussaid, Marco Caponigro, Thomas Chambrion
2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC)
(2019)
Proceedings Paper
Automation & Control Systems
Nabilet Boussaid, Marco Caponigro, Thomas Chambrion
2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC)
(2019)
Proceedings Paper
Automation & Control Systems
Thomas Chambrion, Laurent Thomann
Article
Automation & Control Systems
Thomas Chambrion, Laurent Thomann
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2019)
