Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control
International audience One considers the control problem of an ensemble of Bloch equations (non-interacting half-spins) in a static magnetic field B0. The state M (t, •) belongs to the Sobolev space H 1 ((ω * , ω *), S 2) where the parameter ω ∈ (ω * , ω *) is the Larmor frequency. Previous works ha...
Published in: | Automatica |
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Main Authors: | , , |
Other Authors: | , , , , , , , , , , , , , , |
Format: | Article in Journal/Newspaper |
Language: | English |
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HAL CCSD
2022
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Online Access: | https://minesparis-psl.hal.science/hal-03325203 https://minesparis-psl.hal.science/hal-03325203/document https://minesparis-psl.hal.science/hal-03325203/file/autosam.pdf https://doi.org/10.1016/j.automatica.2022.110529 |
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ftunivparis:oai:HAL:hal-03325203v1 |
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Open Polar |
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Université de Paris: Portail HAL |
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ftunivparis |
language |
English |
topic |
Nonlinear systems Ensemble controllability Quantum systems Adiabatic control Lyapunov feedback stabilization Bloch equations Control of PDEs [SPI.AUTO]Engineering Sciences [physics]/Automatic [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] |
spellingShingle |
Nonlinear systems Ensemble controllability Quantum systems Adiabatic control Lyapunov feedback stabilization Bloch equations Control of PDEs [SPI.AUTO]Engineering Sciences [physics]/Automatic [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] Maciel Neto, Ulisses Alves da Silva, Paulo Sergio Pereira Rouchon, Pierre Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
topic_facet |
Nonlinear systems Ensemble controllability Quantum systems Adiabatic control Lyapunov feedback stabilization Bloch equations Control of PDEs [SPI.AUTO]Engineering Sciences [physics]/Automatic [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] |
description |
International audience One considers the control problem of an ensemble of Bloch equations (non-interacting half-spins) in a static magnetic field B0. The state M (t, •) belongs to the Sobolev space H 1 ((ω * , ω *), S 2) where the parameter ω ∈ (ω * , ω *) is the Larmor frequency. Previous works have constructed a Lyapunov based stabilizing feedback in a convenient H 1-norm that assures local L ∞convergence of the initial state M0(ω) to the south pole, solving locally the approximate steering problem from M0 towards the south pole. However, the corresponding control law contains a comb of periodic π-Rabi pulses (Dirac impulses), corresponding to strongly unbounded control. The present work propose smooth uniformly bounded time-varying controls for this local steering problem, where the Rabi pulses are replaced by adiabatic following smooth pulses. Furthermore, simulations show that this new strategy produces faster convergence, even for initial conditions "relatively far" from the south pole. |
author2 |
Amazônia Azul Tecnologias de Defesa S.A. Polytechnic School of the University of São Paulo (Brazil) Universidade de São Paulo = University of São Paulo (USP) Centre Automatique et Systèmes (CAS) Mines Paris - PSL (École nationale supérieure des mines de Paris) Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL) QUANTum Information Circuits (QUANTIC) Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Sorbonne Université (SU)-Inria de Paris Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS) Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL École normale supérieure - Paris (ENS-PSL) Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-École normale supérieure - Paris (ENS-PSL) Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL Université Paris Sciences et Lettres (PSL) This study was financed in part by the Coordenacao de Aperfei¸coamento de Pessoal de Nıvel Superior -Brazil (CAPES) - Finance Code 001. The second author was partially supported by CNPq, Brazil, Project 305546/2016-3, and by FAPESP, Brazil, Project 18/17463-7. This project has received some funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 884762 ). |
format |
Article in Journal/Newspaper |
author |
Maciel Neto, Ulisses Alves da Silva, Paulo Sergio Pereira Rouchon, Pierre |
author_facet |
Maciel Neto, Ulisses Alves da Silva, Paulo Sergio Pereira Rouchon, Pierre |
author_sort |
Maciel Neto, Ulisses Alves |
title |
Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
title_short |
Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
title_full |
Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
title_fullStr |
Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
title_full_unstemmed |
Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control |
title_sort |
motion planing for an ensemble of bloch equations towards the south pole with smooth bounded control |
publisher |
HAL CCSD |
publishDate |
2022 |
url |
https://minesparis-psl.hal.science/hal-03325203 https://minesparis-psl.hal.science/hal-03325203/document https://minesparis-psl.hal.science/hal-03325203/file/autosam.pdf https://doi.org/10.1016/j.automatica.2022.110529 |
genre |
South pole |
genre_facet |
South pole |
op_source |
ISSN: 0005-1098 Automatica https://minesparis-psl.hal.science/hal-03325203 Automatica, 2022, 145, pp.110529. ⟨10.1016/j.automatica.2022.110529⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.automatica.2022.110529 hal-03325203 https://minesparis-psl.hal.science/hal-03325203 https://minesparis-psl.hal.science/hal-03325203/document https://minesparis-psl.hal.science/hal-03325203/file/autosam.pdf doi:10.1016/j.automatica.2022.110529 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.1016/j.automatica.2022.110529 |
container_title |
Automatica |
container_volume |
145 |
container_start_page |
110529 |
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1799466898913492992 |
spelling |
ftunivparis:oai:HAL:hal-03325203v1 2024-05-19T07:48:36+00:00 Motion planing for an ensemble of Bloch equations towards the south pole with smooth bounded control Maciel Neto, Ulisses Alves da Silva, Paulo Sergio Pereira Rouchon, Pierre Amazônia Azul Tecnologias de Defesa S.A. Polytechnic School of the University of São Paulo (Brazil) Universidade de São Paulo = University of São Paulo (USP) Centre Automatique et Systèmes (CAS) Mines Paris - PSL (École nationale supérieure des mines de Paris) Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL) QUANTum Information Circuits (QUANTIC) Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Sorbonne Université (SU)-Inria de Paris Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de physique de l'ENS - ENS Paris (LPENS) Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL École normale supérieure - Paris (ENS-PSL) Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-École normale supérieure - Paris (ENS-PSL) Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL Université Paris Sciences et Lettres (PSL) This study was financed in part by the Coordenacao de Aperfei¸coamento de Pessoal de Nıvel Superior -Brazil (CAPES) - Finance Code 001. The second author was partially supported by CNPq, Brazil, Project 305546/2016-3, and by FAPESP, Brazil, Project 18/17463-7. This project has received some funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 884762 ). 2022-11 https://minesparis-psl.hal.science/hal-03325203 https://minesparis-psl.hal.science/hal-03325203/document https://minesparis-psl.hal.science/hal-03325203/file/autosam.pdf https://doi.org/10.1016/j.automatica.2022.110529 en eng HAL CCSD Elsevier info:eu-repo/semantics/altIdentifier/doi/10.1016/j.automatica.2022.110529 hal-03325203 https://minesparis-psl.hal.science/hal-03325203 https://minesparis-psl.hal.science/hal-03325203/document https://minesparis-psl.hal.science/hal-03325203/file/autosam.pdf doi:10.1016/j.automatica.2022.110529 info:eu-repo/semantics/OpenAccess ISSN: 0005-1098 Automatica https://minesparis-psl.hal.science/hal-03325203 Automatica, 2022, 145, pp.110529. ⟨10.1016/j.automatica.2022.110529⟩ Nonlinear systems Ensemble controllability Quantum systems Adiabatic control Lyapunov feedback stabilization Bloch equations Control of PDEs [SPI.AUTO]Engineering Sciences [physics]/Automatic [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] info:eu-repo/semantics/article Journal articles 2022 ftunivparis https://doi.org/10.1016/j.automatica.2022.110529 2024-04-23T03:39:32Z International audience One considers the control problem of an ensemble of Bloch equations (non-interacting half-spins) in a static magnetic field B0. The state M (t, •) belongs to the Sobolev space H 1 ((ω * , ω *), S 2) where the parameter ω ∈ (ω * , ω *) is the Larmor frequency. Previous works have constructed a Lyapunov based stabilizing feedback in a convenient H 1-norm that assures local L ∞convergence of the initial state M0(ω) to the south pole, solving locally the approximate steering problem from M0 towards the south pole. However, the corresponding control law contains a comb of periodic π-Rabi pulses (Dirac impulses), corresponding to strongly unbounded control. The present work propose smooth uniformly bounded time-varying controls for this local steering problem, where the Rabi pulses are replaced by adiabatic following smooth pulses. Furthermore, simulations show that this new strategy produces faster convergence, even for initial conditions "relatively far" from the south pole. Article in Journal/Newspaper South pole Université de Paris: Portail HAL Automatica 145 110529 |