Stabilization of One-Dimensional Schrödinger Equation Under Joint Feedback Control with Delayed Observation View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-04

AUTHORS

K. Y. Yang

ABSTRACT

In this paper, we consider a one-dimensional Schrödinger equation under a joint linear feedback control at an arbitrary internal point ξ(0<ξ<1). It is shown that the pointwise control system is asymptotically stable if ξ is either an irrational number or a rational number satisfying ξ≠2l/(2m−1) for any positive integers l,m(1≤l≤m−1); further, the system is exponentially stable if ξ is a rational number satisfying ξ≠2l/(2m−1) for any positive integers l,m(1≤l≤m−1). Moreover, we consider the Schrödinger equation under a joint feedback control where the observation is suffered from a given time delay. A Luenberger observer is designed at the time interval when the observation signal is available, while a predictor is designed at the time interval when the observation signal is not available. A natural control law is constructed based on the estimated state. The closed-loop system is shown to be exponentially stable for the smooth initial value. Finally, numerical simulations demonstrate effectiveness of the dynamic output feedback controller. More... »

PAGES

275-288

References to SciGraph publications

  • 2002-07. Decay Rates for a Beam with Pointwise Force and Moment Feedback in MATHEMATICS OF CONTROL, SIGNALS, AND SYSTEMS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10883-018-9414-y

    DOI

    http://dx.doi.org/10.1007/s10883-018-9414-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1105708945


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Applied Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "North China University of Technology", 
              "id": "https://www.grid.ac/institutes/grid.440852.f", 
              "name": [
                "College of Science, North China University of Technology, Beijing, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yang", 
            "givenName": "K. Y.", 
            "id": "sg:person.012765600143.30", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012765600143.30"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/j.automatica.2009.02.004", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027171733"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s004980200009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043044748", 
              "https://doi.org/10.1007/s004980200009"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0898-1221(04)90132-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046655801"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/cocv/2010044", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1056951842"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/cocv:2008001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1056952584"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/9.182484", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061243233"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/9.186332", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061243263"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/9.566660", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061245187"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/tac.2010.2051070", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061477650"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/0324007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062843851"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/s0363012992240321", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062880951"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/s0363012993250700", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062881002"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/s0363012998349315", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062881515"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.5209/rev_rema.2001.v14.n1.17057", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072708509"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/mmono/018", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1101567795"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-04", 
        "datePublishedReg": "2019-04-01", 
        "description": "In this paper, we consider a one-dimensional Schr\u00f6dinger equation under a joint linear feedback control at an arbitrary internal point \u03be(0<\u03be<1). It is shown that the pointwise control system is asymptotically stable if \u03be is either an irrational number or a rational number satisfying \u03be\u22602l/(2m\u22121) for any positive integers l,m(1\u2264l\u2264m\u22121); further, the system is exponentially stable if \u03be is a rational number satisfying \u03be\u22602l/(2m\u22121) for any positive integers l,m(1\u2264l\u2264m\u22121). Moreover, we consider the Schr\u00f6dinger equation under a joint feedback control where the observation is suffered from a given time delay. A Luenberger observer is designed at the time interval when the observation signal is available, while a predictor is designed at the time interval when the observation signal is not available. A natural control law is constructed based on the estimated state. The closed-loop system is shown to be exponentially stable for the smooth initial value. Finally, numerical simulations demonstrate effectiveness of the dynamic output feedback controller.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s10883-018-9414-y", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.7014258", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1052643", 
            "issn": [
              "1079-2724", 
              "1573-8698"
            ], 
            "name": "Journal of Dynamical and Control Systems", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "25"
          }
        ], 
        "name": "Stabilization of One-Dimensional Schr\u00f6dinger Equation Under Joint Feedback Control with Delayed Observation", 
        "pagination": "275-288", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "a81414895653c717873503819d384d634276213fcdb157599b1ed0308e4cdaf5"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10883-018-9414-y"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1105708945"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10883-018-9414-y", 
          "https://app.dimensions.ai/details/publication/pub.1105708945"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T13:20", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000368_0000000368/records_78965_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs10883-018-9414-y"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10883-018-9414-y'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10883-018-9414-y'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10883-018-9414-y'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10883-018-9414-y'


     

    This table displays all metadata directly associated to this object as RDF triples.

    109 TRIPLES      21 PREDICATES      42 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10883-018-9414-y schema:about anzsrc-for:01
    2 anzsrc-for:0102
    3 schema:author N6310026c9164459884d4cbb155c37f8b
    4 schema:citation sg:pub.10.1007/s004980200009
    5 https://doi.org/10.1016/j.automatica.2009.02.004
    6 https://doi.org/10.1016/s0898-1221(04)90132-0
    7 https://doi.org/10.1051/cocv/2010044
    8 https://doi.org/10.1051/cocv:2008001
    9 https://doi.org/10.1090/mmono/018
    10 https://doi.org/10.1109/9.182484
    11 https://doi.org/10.1109/9.186332
    12 https://doi.org/10.1109/9.566660
    13 https://doi.org/10.1109/tac.2010.2051070
    14 https://doi.org/10.1137/0324007
    15 https://doi.org/10.1137/s0363012992240321
    16 https://doi.org/10.1137/s0363012993250700
    17 https://doi.org/10.1137/s0363012998349315
    18 https://doi.org/10.5209/rev_rema.2001.v14.n1.17057
    19 schema:datePublished 2019-04
    20 schema:datePublishedReg 2019-04-01
    21 schema:description In this paper, we consider a one-dimensional Schrödinger equation under a joint linear feedback control at an arbitrary internal point ξ(0<ξ<1). It is shown that the pointwise control system is asymptotically stable if ξ is either an irrational number or a rational number satisfying ξ≠2l/(2m−1) for any positive integers l,m(1≤l≤m−1); further, the system is exponentially stable if ξ is a rational number satisfying ξ≠2l/(2m−1) for any positive integers l,m(1≤l≤m−1). Moreover, we consider the Schrödinger equation under a joint feedback control where the observation is suffered from a given time delay. A Luenberger observer is designed at the time interval when the observation signal is available, while a predictor is designed at the time interval when the observation signal is not available. A natural control law is constructed based on the estimated state. The closed-loop system is shown to be exponentially stable for the smooth initial value. Finally, numerical simulations demonstrate effectiveness of the dynamic output feedback controller.
    22 schema:genre research_article
    23 schema:inLanguage en
    24 schema:isAccessibleForFree false
    25 schema:isPartOf N5eec02bfa8e4440ca9ff5f92dcf1ecc5
    26 N96c07d9d6991467bbd23baefd700510e
    27 sg:journal.1052643
    28 schema:name Stabilization of One-Dimensional Schrödinger Equation Under Joint Feedback Control with Delayed Observation
    29 schema:pagination 275-288
    30 schema:productId N068072472c3b4c16a4cb620bba1c3756
    31 N5343f4e110fb44119824e0b586423b48
    32 Nb2151985831349d882b0d308e33a6912
    33 schema:sameAs https://app.dimensions.ai/details/publication/pub.1105708945
    34 https://doi.org/10.1007/s10883-018-9414-y
    35 schema:sdDatePublished 2019-04-11T13:20
    36 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    37 schema:sdPublisher N84ae8e21dacf4e4b93742332603ef8b3
    38 schema:url https://link.springer.com/10.1007%2Fs10883-018-9414-y
    39 sgo:license sg:explorer/license/
    40 sgo:sdDataset articles
    41 rdf:type schema:ScholarlyArticle
    42 N068072472c3b4c16a4cb620bba1c3756 schema:name readcube_id
    43 schema:value a81414895653c717873503819d384d634276213fcdb157599b1ed0308e4cdaf5
    44 rdf:type schema:PropertyValue
    45 N5343f4e110fb44119824e0b586423b48 schema:name doi
    46 schema:value 10.1007/s10883-018-9414-y
    47 rdf:type schema:PropertyValue
    48 N5eec02bfa8e4440ca9ff5f92dcf1ecc5 schema:issueNumber 2
    49 rdf:type schema:PublicationIssue
    50 N6310026c9164459884d4cbb155c37f8b rdf:first sg:person.012765600143.30
    51 rdf:rest rdf:nil
    52 N84ae8e21dacf4e4b93742332603ef8b3 schema:name Springer Nature - SN SciGraph project
    53 rdf:type schema:Organization
    54 N96c07d9d6991467bbd23baefd700510e schema:volumeNumber 25
    55 rdf:type schema:PublicationVolume
    56 Nb2151985831349d882b0d308e33a6912 schema:name dimensions_id
    57 schema:value pub.1105708945
    58 rdf:type schema:PropertyValue
    59 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    60 schema:name Mathematical Sciences
    61 rdf:type schema:DefinedTerm
    62 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
    63 schema:name Applied Mathematics
    64 rdf:type schema:DefinedTerm
    65 sg:grant.7014258 http://pending.schema.org/fundedItem sg:pub.10.1007/s10883-018-9414-y
    66 rdf:type schema:MonetaryGrant
    67 sg:journal.1052643 schema:issn 1079-2724
    68 1573-8698
    69 schema:name Journal of Dynamical and Control Systems
    70 rdf:type schema:Periodical
    71 sg:person.012765600143.30 schema:affiliation https://www.grid.ac/institutes/grid.440852.f
    72 schema:familyName Yang
    73 schema:givenName K. Y.
    74 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012765600143.30
    75 rdf:type schema:Person
    76 sg:pub.10.1007/s004980200009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043044748
    77 https://doi.org/10.1007/s004980200009
    78 rdf:type schema:CreativeWork
    79 https://doi.org/10.1016/j.automatica.2009.02.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027171733
    80 rdf:type schema:CreativeWork
    81 https://doi.org/10.1016/s0898-1221(04)90132-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046655801
    82 rdf:type schema:CreativeWork
    83 https://doi.org/10.1051/cocv/2010044 schema:sameAs https://app.dimensions.ai/details/publication/pub.1056951842
    84 rdf:type schema:CreativeWork
    85 https://doi.org/10.1051/cocv:2008001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1056952584
    86 rdf:type schema:CreativeWork
    87 https://doi.org/10.1090/mmono/018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101567795
    88 rdf:type schema:CreativeWork
    89 https://doi.org/10.1109/9.182484 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061243233
    90 rdf:type schema:CreativeWork
    91 https://doi.org/10.1109/9.186332 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061243263
    92 rdf:type schema:CreativeWork
    93 https://doi.org/10.1109/9.566660 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061245187
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.1109/tac.2010.2051070 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061477650
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.1137/0324007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062843851
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.1137/s0363012992240321 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062880951
    100 rdf:type schema:CreativeWork
    101 https://doi.org/10.1137/s0363012993250700 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062881002
    102 rdf:type schema:CreativeWork
    103 https://doi.org/10.1137/s0363012998349315 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062881515
    104 rdf:type schema:CreativeWork
    105 https://doi.org/10.5209/rev_rema.2001.v14.n1.17057 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072708509
    106 rdf:type schema:CreativeWork
    107 https://www.grid.ac/institutes/grid.440852.f schema:alternateName North China University of Technology
    108 schema:name College of Science, North China University of Technology, Beijing, China
    109 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...