Optimality Conditions and Synthesis for the Minimum Time Problem View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2000-06

AUTHORS

Piermarco Cannarsa, Hélène Frankowska, Carlo Sinestrari

ABSTRACT

We study the minimum time optimal control problem for a nonlinear system in Rn with a general target. Necessary and sufficient optimality conditions are obtained. In particular, we describe a class of costates that are included in the superdifferential of the minimum time function, even in the case when this function is only lower semicontinuous. Two set-valued maps are constructed to provide time optimal synthesis. More... »

PAGES

127-148

References to SciGraph publications

  • 1989-01. Optimal trajectories associated with a solution of the contingent Hamilton-Jacobi equation in APPLIED MATHEMATICS & OPTIMIZATION
  • 1990-05. Maximum principle, dynamic programming, and their connection in deterministic control in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1995-06. Convexity properties of the minimum time function in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 1997-08. Lipschitz Continuity of the Value Function in Optimal Control in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1008726610555

    DOI

    http://dx.doi.org/10.1023/a:1008726610555

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1022918159


    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": "University of Rome Tor Vergata", 
              "id": "https://www.grid.ac/institutes/grid.6530.0", 
              "name": [
                "Dipartimento di Matematica, Universit\u00e0 di Roma 'Tor Vergata\", Via della Ricerca Scientifica, 00133, Rome, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Cannarsa", 
            "givenName": "Piermarco", 
            "id": "sg:person.014257010655.09", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014257010655.09"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Paris Dauphine University", 
              "id": "https://www.grid.ac/institutes/grid.11024.36", 
              "name": [
                "Centre de Recherche 'Viabilit\u00e9, Jeux, Contr\u00f4le\", Universit\u00e9 Paris-Dauphine and CNRS, Place M. de Lattre de Tassigny, F-75775, Paris Cedex 16, France"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Frankowska", 
            "givenName": "H\u00e9l\u00e8ne", 
            "id": "sg:person.014732773366.11", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014732773366.11"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Rome Tor Vergata", 
              "id": "https://www.grid.ac/institutes/grid.6530.0", 
              "name": [
                "Dipartimento di Matematica, Universit\u00e0 di Roma 'Tor Vergata\", Via della Ricerca Scientifica, 00133, Rome, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Sinestrari", 
            "givenName": "Carlo", 
            "id": "sg:person.010746770411.97", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010746770411.97"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01189393", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000572512", 
              "https://doi.org/10.1007/bf01189393"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01189393", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000572512", 
              "https://doi.org/10.1007/bf01189393"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1022683628650", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012240288", 
              "https://doi.org/10.1023/a:1022683628650"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01102352", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024455157", 
              "https://doi.org/10.1007/bf01102352"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01102352", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024455157", 
              "https://doi.org/10.1007/bf01102352"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01448202", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027946982", 
              "https://doi.org/10.1007/bf01448202"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01448202", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027946982", 
              "https://doi.org/10.1007/bf01448202"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0021-8928(70)90060-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043091224"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0021-8928(70)90060-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043091224"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/0325071", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062843995"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/0327010", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062844109"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/0328053", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062844228"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/0329068", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062844322"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/dcds.1995.1.285", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071732553"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.5802/aif.319", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1073138938"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2000-06", 
        "datePublishedReg": "2000-06-01", 
        "description": "We study the minimum time optimal control problem for a nonlinear system in Rn with a general target. Necessary and sufficient optimality conditions are obtained. In particular, we describe a class of costates that are included in the superdifferential of the minimum time function, even in the case when this function is only lower semicontinuous. Two set-valued maps are constructed to provide time optimal synthesis.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1023/a:1008726610555", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1327872", 
            "issn": [
              "0927-6947", 
              "1572-932X"
            ], 
            "name": "Set-Valued Analysis", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1-2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "8"
          }
        ], 
        "name": "Optimality Conditions and Synthesis for the Minimum Time Problem", 
        "pagination": "127-148", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "6d2fd6f4219f97fbb231399e833fff9943f28809ca1162b4d61461790e82149e"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1023/a:1008726610555"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1022918159"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1023/a:1008726610555", 
          "https://app.dimensions.ai/details/publication/pub.1022918159"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T01:04", 
        "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/v90/0000000001_0000000264/records_8697_00000499.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1023/A:1008726610555"
      }
    ]
     

    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.10.1023/a:1008726610555'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1023/a:1008726610555'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1008726610555'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1008726610555'


     

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

    115 TRIPLES      21 PREDICATES      38 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1023/a:1008726610555 schema:about anzsrc-for:01
    2 anzsrc-for:0102
    3 schema:author N274033362ce24026ae849281de0fb80d
    4 schema:citation sg:pub.10.1007/bf01102352
    5 sg:pub.10.1007/bf01189393
    6 sg:pub.10.1007/bf01448202
    7 sg:pub.10.1023/a:1022683628650
    8 https://doi.org/10.1016/0021-8928(70)90060-2
    9 https://doi.org/10.1137/0325071
    10 https://doi.org/10.1137/0327010
    11 https://doi.org/10.1137/0328053
    12 https://doi.org/10.1137/0329068
    13 https://doi.org/10.3934/dcds.1995.1.285
    14 https://doi.org/10.5802/aif.319
    15 schema:datePublished 2000-06
    16 schema:datePublishedReg 2000-06-01
    17 schema:description We study the minimum time optimal control problem for a nonlinear system in Rn with a general target. Necessary and sufficient optimality conditions are obtained. In particular, we describe a class of costates that are included in the superdifferential of the minimum time function, even in the case when this function is only lower semicontinuous. Two set-valued maps are constructed to provide time optimal synthesis.
    18 schema:genre research_article
    19 schema:inLanguage en
    20 schema:isAccessibleForFree false
    21 schema:isPartOf Ncb64019aaf7a48d0bb2b6def379b2bd6
    22 Ne61e949c26ff4f0c94539d7d5c504b4d
    23 sg:journal.1327872
    24 schema:name Optimality Conditions and Synthesis for the Minimum Time Problem
    25 schema:pagination 127-148
    26 schema:productId N087a95c390274baaaa70939ae79c880c
    27 N9873b2590f4b4cd68f6872fb817067ef
    28 Nd4358126320f4f4fba17e401d6f6f3dd
    29 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022918159
    30 https://doi.org/10.1023/a:1008726610555
    31 schema:sdDatePublished 2019-04-11T01:04
    32 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    33 schema:sdPublisher Nbcff52cbaf6f483c8856935c9945bac9
    34 schema:url http://link.springer.com/10.1023/A:1008726610555
    35 sgo:license sg:explorer/license/
    36 sgo:sdDataset articles
    37 rdf:type schema:ScholarlyArticle
    38 N087a95c390274baaaa70939ae79c880c schema:name doi
    39 schema:value 10.1023/a:1008726610555
    40 rdf:type schema:PropertyValue
    41 N274033362ce24026ae849281de0fb80d rdf:first sg:person.014257010655.09
    42 rdf:rest N8e6837c4abd340bbad03485645030979
    43 N4b8fd97b34c54226a2d9b543a5b568ec rdf:first sg:person.010746770411.97
    44 rdf:rest rdf:nil
    45 N8e6837c4abd340bbad03485645030979 rdf:first sg:person.014732773366.11
    46 rdf:rest N4b8fd97b34c54226a2d9b543a5b568ec
    47 N9873b2590f4b4cd68f6872fb817067ef schema:name dimensions_id
    48 schema:value pub.1022918159
    49 rdf:type schema:PropertyValue
    50 Nbcff52cbaf6f483c8856935c9945bac9 schema:name Springer Nature - SN SciGraph project
    51 rdf:type schema:Organization
    52 Ncb64019aaf7a48d0bb2b6def379b2bd6 schema:issueNumber 1-2
    53 rdf:type schema:PublicationIssue
    54 Nd4358126320f4f4fba17e401d6f6f3dd schema:name readcube_id
    55 schema:value 6d2fd6f4219f97fbb231399e833fff9943f28809ca1162b4d61461790e82149e
    56 rdf:type schema:PropertyValue
    57 Ne61e949c26ff4f0c94539d7d5c504b4d schema:volumeNumber 8
    58 rdf:type schema:PublicationVolume
    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:journal.1327872 schema:issn 0927-6947
    66 1572-932X
    67 schema:name Set-Valued Analysis
    68 rdf:type schema:Periodical
    69 sg:person.010746770411.97 schema:affiliation https://www.grid.ac/institutes/grid.6530.0
    70 schema:familyName Sinestrari
    71 schema:givenName Carlo
    72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010746770411.97
    73 rdf:type schema:Person
    74 sg:person.014257010655.09 schema:affiliation https://www.grid.ac/institutes/grid.6530.0
    75 schema:familyName Cannarsa
    76 schema:givenName Piermarco
    77 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014257010655.09
    78 rdf:type schema:Person
    79 sg:person.014732773366.11 schema:affiliation https://www.grid.ac/institutes/grid.11024.36
    80 schema:familyName Frankowska
    81 schema:givenName Hélène
    82 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014732773366.11
    83 rdf:type schema:Person
    84 sg:pub.10.1007/bf01102352 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024455157
    85 https://doi.org/10.1007/bf01102352
    86 rdf:type schema:CreativeWork
    87 sg:pub.10.1007/bf01189393 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000572512
    88 https://doi.org/10.1007/bf01189393
    89 rdf:type schema:CreativeWork
    90 sg:pub.10.1007/bf01448202 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027946982
    91 https://doi.org/10.1007/bf01448202
    92 rdf:type schema:CreativeWork
    93 sg:pub.10.1023/a:1022683628650 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012240288
    94 https://doi.org/10.1023/a:1022683628650
    95 rdf:type schema:CreativeWork
    96 https://doi.org/10.1016/0021-8928(70)90060-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043091224
    97 rdf:type schema:CreativeWork
    98 https://doi.org/10.1137/0325071 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062843995
    99 rdf:type schema:CreativeWork
    100 https://doi.org/10.1137/0327010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062844109
    101 rdf:type schema:CreativeWork
    102 https://doi.org/10.1137/0328053 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062844228
    103 rdf:type schema:CreativeWork
    104 https://doi.org/10.1137/0329068 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062844322
    105 rdf:type schema:CreativeWork
    106 https://doi.org/10.3934/dcds.1995.1.285 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071732553
    107 rdf:type schema:CreativeWork
    108 https://doi.org/10.5802/aif.319 schema:sameAs https://app.dimensions.ai/details/publication/pub.1073138938
    109 rdf:type schema:CreativeWork
    110 https://www.grid.ac/institutes/grid.11024.36 schema:alternateName Paris Dauphine University
    111 schema:name Centre de Recherche 'Viabilité, Jeux, Contrôle", Université Paris-Dauphine and CNRS, Place M. de Lattre de Tassigny, F-75775, Paris Cedex 16, France
    112 rdf:type schema:Organization
    113 https://www.grid.ac/institutes/grid.6530.0 schema:alternateName University of Rome Tor Vergata
    114 schema:name Dipartimento di Matematica, Università di Roma 'Tor Vergata", Via della Ricerca Scientifica, 00133, Rome, Italy
    115 rdf:type schema:Organization
     




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


    ...