The Experts below are selected from a list of 63606 Experts worldwide ranked by ideXlab platform
Mario Sigalotti - One of the best experts on this subject based on the ideXlab platform.
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multi input schrodinger equation Controllability tracking and application to the quantum angular momentum
Journal of Differential Equations, 2014Co-Authors: Ugo Boscain, Marco Caponigro, Mario SigalottiAbstract:Abstract We present a sufficient condition for approximate Controllability of the bilinear discrete-spectrum Schrodinger equation in the multi-input case. The Controllability result extends to simultaneous Controllability, approximate Controllability in H s , and tracking in modulus. The sufficient condition is more general than those present in the literature even in the single-input case and allows the spectrum of the uncontrolled operator to be very degenerate (e.g. to have multiple eigenvalues or equal gaps among different pairs of eigenvalues). We apply the general result to a rotating polar linear molecule, driven by three orthogonal external fields. A remarkable property of this model is the presence of infinitely many degeneracies and resonances in the spectrum.
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A weak spectral condition for the Controllability of the bilinear Schrödinger equation with application to the control of a rotating planar molecule
Communications in Mathematical Physics, 2012Co-Authors: Ugo Boscain, Marco Caponigro, Thomas Chambrion, Mario SigalottiAbstract:In this paper we prove an approximate Controllability result for the bilinear Schrödinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schrödinger operator than those present in the literature. The control operator is not required to be bounded and we are able to extend the Controllability result to the density matrices. The proof is based on fine Controllability properties of the finite dimensional Galerkin approximations and allows to get estimates for the $L^{1}$ norm of the control. The general Controllability result is applied to the problem of controlling the rotation of a bipolar rigid molecule confined on a plane by means of two orthogonal external fields.
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a weak spectral condition for the Controllability of the bilinear schr odinger equation with application to the control of a rotating planar molecule
arXiv: Optimization and Control, 2011Co-Authors: Ugo Boscain, Marco Caponigro, Thomas Chambrion, Mario SigalottiAbstract:In this paper we prove an approximate Controllability result for the bilinear Schrodinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schrodinger operator than those present in the literature. The control operator is not required to be bounded and we are able to extend the Controllability result to the density matrices. The proof is based on fine Controllability properties of the finite dimensional Galerkin approximations and allows to get estimates for the $L^{1}$ norm of the control. The general Controllability result is applied to the problem of controlling the rotation of a bipolar rigid molecule confined on a plane by means of two orthogonal external fields.
Riccardo Muradore - One of the best experts on this subject based on the ideXlab platform.
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minimal Controllability time for systems with nonlinear drift under a compact convex state constraint
Automatica, 2021Co-Authors: Viktor Bezborodov, Luca Di Persio, Riccardo MuradoreAbstract:Abstract In this paper we estimate the minimal Controllability time for a class of non-linear control systems with a bounded convex state constraint. An explicit expression is given for the Controllability time if the image of the control matrix is of co-dimension one. A lower bound for the Controllability time is given in the general case. The technique is based on finding a lower dimension system with the similar Controllability properties as the original system. The controls corresponding to the minimal time, or time close to the minimal one, are discussed and computed analytically. The effectiveness of the proposed approach is illustrated by a few examples.
Ugo Boscain - One of the best experts on this subject based on the ideXlab platform.
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multi input schrodinger equation Controllability tracking and application to the quantum angular momentum
Journal of Differential Equations, 2014Co-Authors: Ugo Boscain, Marco Caponigro, Mario SigalottiAbstract:Abstract We present a sufficient condition for approximate Controllability of the bilinear discrete-spectrum Schrodinger equation in the multi-input case. The Controllability result extends to simultaneous Controllability, approximate Controllability in H s , and tracking in modulus. The sufficient condition is more general than those present in the literature even in the single-input case and allows the spectrum of the uncontrolled operator to be very degenerate (e.g. to have multiple eigenvalues or equal gaps among different pairs of eigenvalues). We apply the general result to a rotating polar linear molecule, driven by three orthogonal external fields. A remarkable property of this model is the presence of infinitely many degeneracies and resonances in the spectrum.
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A weak spectral condition for the Controllability of the bilinear Schrödinger equation with application to the control of a rotating planar molecule
Communications in Mathematical Physics, 2012Co-Authors: Ugo Boscain, Marco Caponigro, Thomas Chambrion, Mario SigalottiAbstract:In this paper we prove an approximate Controllability result for the bilinear Schrödinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schrödinger operator than those present in the literature. The control operator is not required to be bounded and we are able to extend the Controllability result to the density matrices. The proof is based on fine Controllability properties of the finite dimensional Galerkin approximations and allows to get estimates for the $L^{1}$ norm of the control. The general Controllability result is applied to the problem of controlling the rotation of a bipolar rigid molecule confined on a plane by means of two orthogonal external fields.
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a weak spectral condition for the Controllability of the bilinear schr odinger equation with application to the control of a rotating planar molecule
arXiv: Optimization and Control, 2011Co-Authors: Ugo Boscain, Marco Caponigro, Thomas Chambrion, Mario SigalottiAbstract:In this paper we prove an approximate Controllability result for the bilinear Schrodinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schrodinger operator than those present in the literature. The control operator is not required to be bounded and we are able to extend the Controllability result to the density matrices. The proof is based on fine Controllability properties of the finite dimensional Galerkin approximations and allows to get estimates for the $L^{1}$ norm of the control. The general Controllability result is applied to the problem of controlling the rotation of a bipolar rigid molecule confined on a plane by means of two orthogonal external fields.
Viktor Bezborodov - One of the best experts on this subject based on the ideXlab platform.
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minimal Controllability time for systems with nonlinear drift under a compact convex state constraint
Automatica, 2021Co-Authors: Viktor Bezborodov, Luca Di Persio, Riccardo MuradoreAbstract:Abstract In this paper we estimate the minimal Controllability time for a class of non-linear control systems with a bounded convex state constraint. An explicit expression is given for the Controllability time if the image of the control matrix is of co-dimension one. A lower bound for the Controllability time is given in the general case. The technique is based on finding a lower dimension system with the similar Controllability properties as the original system. The controls corresponding to the minimal time, or time close to the minimal one, are discussed and computed analytically. The effectiveness of the proposed approach is illustrated by a few examples.
Xinming Cheng - One of the best experts on this subject based on the ideXlab platform.
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Controllability analysis of complex valued impulsive systems with time varying delays
Communications in Nonlinear Science and Numerical Simulation, 2020Co-Authors: Jiayuan Yan, Zhihong Guan, Xinming ChengAbstract:Abstract This paper studies the Controllability of complex-valued impulsive systems with time-varying delays in control input. The impulsive systems considered here have a complex-valued state space, for some typical examples such as biological neural networks and quantum systems can be described by such systems. Using the method of variation of parameters, an explicit expression of the solution for the given system is established. Based on the solution so obtained, several Controllability criteria are presented for such systems. Necessary and sufficient conditions for Controllability are further derived for the time-invariant case. It is shown that Controllability of such systems is dependent on the impulsive function in discrete time, the system matrices in continuous time, and the time delay in control. Three numerical examples are presented to demonstrate the effectiveness of the developed Controllability results.
