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Rapid Lyapunov control of finite-dimensional quantum systems

Kuang, Sen; Dong, Daoyi; Petersen, Ian

Description

Rapid state control of quantum systems is significant in reducing the influence of relaxation or decoherence caused by the environment and enhancing the capability in dealing with uncertainties in the model and control process. Bang–bang Lyapunov control can speed up the control process, but cannot guarantee convergence to a target state. This paper proposes two classes of new Lyapunov control methods that can achieve rapidly convergent control for quantum states. One class is switching...[Show more]

dc.contributor.authorKuang, Sen
dc.contributor.authorDong, Daoyi
dc.contributor.authorPetersen, Ian
dc.date.accessioned2021-09-08T23:36:22Z
dc.identifier.issn0005-1098
dc.identifier.urihttp://hdl.handle.net/1885/247708
dc.description.abstractRapid state control of quantum systems is significant in reducing the influence of relaxation or decoherence caused by the environment and enhancing the capability in dealing with uncertainties in the model and control process. Bang–bang Lyapunov control can speed up the control process, but cannot guarantee convergence to a target state. This paper proposes two classes of new Lyapunov control methods that can achieve rapidly convergent control for quantum states. One class is switching Lyapunov control where the control law is designed by switching between bang–bang Lyapunov control and standard Lyapunov control. The other class is approximate bang–bang Lyapunov control where we propose two special control functions which are continuously differentiable and yet have a bang–bang type property. Related stability results are given and a construction method for the degrees of freedom in the Lyapunov function is presented to guarantee rapid convergence to a target eigenstate being isolated in the invariant set. Several numerical examples demonstrate that the proposed methods can achieve improved performance for rapid state control of quantum systems.
dc.description.sponsorshipThis work was supported by the Anhui Provincial Natural Science Foundation (1708085MF144), the Fundamental Research Funds for the Central Universities, and the Australian Research Council (DP130101658, FL110100020
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherElsevier
dc.rights© 2017 Elsevier Ltd
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.sourceAutomatica
dc.subjectQuantum systems
dc.subjectSwitching control
dc.subjectApproximate bang–bang control
dc.subjectRapid Lyapunov control
dc.titleRapid Lyapunov control of finite-dimensional quantum systems
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume81
dc.date.issued2017
local.identifier.absfor090602 - Control Systems, Robotics and Automation
local.identifier.ariespublicationu5357342xPUB321
local.publisher.urlhttps://www.elsevier.com/en-au
local.type.statusAccepted Version
local.contributor.affiliationKuang, Sen, University of New South Wales at Canberra
local.contributor.affiliationDong, Daoyi, University of New South Wales
local.contributor.affiliationPetersen, Ian, College of Engineering and Computer Science, ANU
dc.relationhttp://purl.org/au-research/grants/arc/DP130101658
dc.relationhttp://purl.org/au-research/grants/arc/FL110100020
local.bibliographicCitation.startpage164
local.bibliographicCitation.lastpage175
local.identifier.doi10.1016/j.automatica.2017.02.041
local.identifier.absseo970109 - Expanding Knowledge in Engineering
dc.date.updated2020-11-23T11:00:50Z
local.identifier.scopusID2-s2.0-85018471108
local.identifier.thomsonID000403513900019
dcterms.accessRightsOpen Access
dc.provenancehttps://v2.sherpa.ac.uk/id/publication/4278..."The Accepted Version can be archived in an Institutional Repository. 24 Months. CC BY-NC-ND." from SHERPA/RoMEO site (as at 14/09/2021).
dc.rights.licenseCC BY-NC-ND
CollectionsANU Research Publications

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