<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of inria-00271155</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-19T20:18:39+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Using switching detection and variational equations for the shooting method</title>
            <author role="aut">
              <persName>
                <forename type="first">Pierre</forename>
                <surname>Martinon</surname>
              </persName>
              <email type="md5">70cc87631e2bdb2c802f62fe762e0b88</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">pierre-martinon</idno>
              <idno type="idhal" notation="numeric">1835</idno>
              <idno type="halauthorid" notation="string">19312-1835</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-0571-2376</idno>
              <idno type="IDREF">https://www.idref.fr/096316624</idno>
              <affiliation ref="#struct-89626"/>
              <affiliation ref="#struct-56041"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Joseph</forename>
                <surname>Gergaud</surname>
              </persName>
              <email type="md5">984e496deaceab431452f6015a50c2f6</email>
              <email type="domain">enseeiht.fr</email>
              <idno type="idhal" notation="string">joseph-gergaud</idno>
              <idno type="idhal" notation="numeric">185036</idno>
              <idno type="halauthorid" notation="string">21409-185036</idno>
              <idno type="IDREF">https://www.idref.fr/07924453X</idno>
              <orgName ref="#struct-448187"/>
              <affiliation ref="#struct-1001830"/>
              <affiliation ref="#struct-448187"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Pierre</forename>
                <surname>Martinon</surname>
              </persName>
              <email type="md5">70cc87631e2bdb2c802f62fe762e0b88</email>
              <email type="domain">inria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2008-04-08 13:15:01</date>
              <date type="whenModified">2025-10-22 18:04:07</date>
              <date type="whenReleased">2008-04-08 14:10:22</date>
              <date type="whenProduced">2007</date>
              <date type="whenEndEmbargoed">2008-04-08</date>
              <ref type="file" target="https://inria.hal.science/inria-00271155v1/document">
                <date notBefore="2008-04-08"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://inria.hal.science/inria-00271155v1/file/Martinon-Gergaud-OCAM2006-preprint.pdf" id="file-271155-335282">
                <date notBefore="2008-04-08"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="108521">
                <persName>
                  <forename>Pierre</forename>
                  <surname>Martinon</surname>
                </persName>
                <email type="md5">70cc87631e2bdb2c802f62fe762e0b88</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">inria-00271155</idno>
            <idno type="halUri">https://inria.hal.science/inria-00271155</idno>
            <idno type="halBibtex">martinon:inria-00271155</idno>
            <idno type="halRefHtml">&lt;i&gt;Optimal Control Applications and Methods&lt;/i&gt;, 2007, 28 (2), pp.95-116</idno>
            <idno type="halRef">Optimal Control Applications and Methods, 2007, 28 (2), pp.95-116</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-271155-335282"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="UNIV-TLSE2">Université Toulouse 2</idno>
            <idno type="stamp" n="UNIV-TLSE3">Université de Toulouse</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="INRIA-SACLAY" corresp="INRIA">INRIA Saclay - Ile de France</idno>
            <idno type="stamp" n="X-CMAP" corresp="X">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="X-DEP-MATHA">Département de mathématiques appliquées de l’École polytechnique</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="CMAP">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="UT1-CAPITOLE">Université Toulouse 1 Capitole</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="IRIT">IRIT - Institut de Recherche en Informatique de Toulouse</idno>
            <idno type="stamp" n="IRIT-APO" corresp="IRIT">Algorithmes Parallèles et Optimisation</idno>
            <idno type="stamp" n="IRIT-CISO" corresp="IRIT">Calcul Intensif, Simulation, Optimisation</idno>
            <idno type="stamp" n="IRIT-INPT">IRIT - Toulouse INP</idno>
            <idno type="stamp" n="TOULOUSE-INP">Toulouse - INP</idno>
            <idno type="stamp" n="UNIV-UT3">Université Toulouse 3</idno>
            <idno type="stamp" n="UT3-INP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="UT3-TOULOUSEINP">Université de Toulouse / Toulouse INP</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Using switching detection and variational equations for the shooting method</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Pierre</forename>
                    <surname>Martinon</surname>
                  </persName>
                  <email type="md5">70cc87631e2bdb2c802f62fe762e0b88</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">pierre-martinon</idno>
                  <idno type="idhal" notation="numeric">1835</idno>
                  <idno type="halauthorid" notation="string">19312-1835</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-0571-2376</idno>
                  <idno type="IDREF">https://www.idref.fr/096316624</idno>
                  <affiliation ref="#struct-89626"/>
                  <affiliation ref="#struct-56041"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Joseph</forename>
                    <surname>Gergaud</surname>
                  </persName>
                  <email type="md5">984e496deaceab431452f6015a50c2f6</email>
                  <email type="domain">enseeiht.fr</email>
                  <idno type="idhal" notation="string">joseph-gergaud</idno>
                  <idno type="idhal" notation="numeric">185036</idno>
                  <idno type="halauthorid" notation="string">21409-185036</idno>
                  <idno type="IDREF">https://www.idref.fr/07924453X</idno>
                  <orgName ref="#struct-448187"/>
                  <affiliation ref="#struct-1001830"/>
                  <affiliation ref="#struct-448187"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">17660</idno>
                <idno type="issn">0143-2087</idno>
                <idno type="eissn">1099-1514</idno>
                <title level="j">Optimal Control Applications and Methods</title>
                <imprint>
                  <publisher>Wiley</publisher>
                  <biblScope unit="volume">28</biblScope>
                  <biblScope unit="issue">2</biblScope>
                  <biblScope unit="pp">95-116</biblScope>
                  <date type="datePub">2007</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Shooting method</term>
                <term xml:lang="en">Jacobian evaluation</term>
                <term xml:lang="en">switching detection</term>
                <term xml:lang="en">variational equations</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We study in this paper the resolution by single shooting of an optimal control problem with a bang-bang control involving a large number of commutations. We focus on the handling of these commutations regarding the precise computation of the shooting function and its Jacobian. We first observe the impact of a switching detection algorithm on the shooting method results. Then, we study the computation of the Jacobian of the shooting function, by comparing classical finite differences to a formulation using the variational equations. We consider as an application a low thrust orbital transfer with payload maximization. This kind of problem presents a discontinuous optimal control, and involves up to 1800 commutations for the lowest thrust. Copyright c 2000 John Wiley &amp; Sons, Ltd.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-89626" status="VALID">
          <idno type="IdRef">197373461</idno>
          <idno type="ISNI">000000010944436X</idno>
          <idno type="RNSR">199719340P</idno>
          <idno type="ROR">https://ror.org/012e1xn46</idno>
          <idno type="Wikidata">Q16008922</idno>
          <orgName>Centre de Mathématiques Appliquées de l'Ecole polytechnique</orgName>
          <orgName type="acronym">CMAP</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://cmap.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-56041" status="OLD">
          <idno type="RNSR">200718995W</idno>
          <orgName>Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems</orgName>
          <orgName type="acronym">Commands</orgName>
          <desc>
            <address>
              <addrLine>Centre de Mathématiques Appliquées Ecole Polytechnique Route de Saclay 91128 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/commands</ref>
          </desc>
          <listRelation>
            <relation active="#struct-89626" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-300340" type="indirect"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="indirect"/>
            <relation active="#struct-118511" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-1001830" status="OLD">
          <orgName>Algorithmes Parallèles et Optimisation</orgName>
          <orgName type="acronym">IRIT-APO</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>Institut de recherche en informatique de Toulouse - IRIT2 rue Charles Camichel 31071 Toulouse Cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.irit.fr/departement/calcul-intensif-simulation-optimisation/equipe-apo/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-34499" type="direct"/>
            <relation active="#struct-81148" type="indirect"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-217752" type="indirect"/>
            <relation name="UMR5505 / URA1399" active="#struct-441569" type="indirect"/>
            <relation active="#struct-448187" type="indirect"/>
            <relation active="#struct-1149079" type="indirect"/>
            <relation name="FED4171" active="#struct-217752" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-448187" status="VALID">
          <idno type="IdRef">026388820</idno>
          <idno type="ISNI">0000000121766169</idno>
          <idno type="ROR">https://ror.org/033p9g875</idno>
          <orgName>Institut National Polytechnique (Toulouse)</orgName>
          <orgName type="acronym">Toulouse INP</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.inp-toulouse.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-118511" status="VALID">
          <idno type="RNSR">200818248E</idno>
          <idno type="ROR">https://ror.org/0315e5x55</idno>
          <orgName>Centre Inria de Saclay</orgName>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'OrvesBâtiment Alan TuringCampus de l'École Polytechnique91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/saclay</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-34499" status="OLD">
          <idno type="IdRef">030947448</idno>
          <idno type="ISNI">0000000121927225</idno>
          <idno type="RNSR">199511949P</idno>
          <idno type="ROR">https://ror.org/01rx4qw44</idno>
          <orgName>Institut de recherche en informatique de Toulouse</orgName>
          <orgName type="acronym">IRIT</orgName>
          <date type="start">1990-01-01</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 Route de Narbonne, F-31062 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.irit.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-217752" type="direct"/>
            <relation name="UMR5505 / URA1399" active="#struct-441569" type="direct"/>
            <relation active="#struct-448187" type="direct"/>
            <relation active="#struct-1149079" type="direct"/>
            <relation name="FED4171" active="#struct-217752" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-81148" status="VALID">
          <idno type="IdRef">026404354</idno>
          <idno type="ISNI">0000000121902837</idno>
          <idno type="ROR">https://ror.org/0443n9e75</idno>
          <orgName>Université Toulouse Capitole</orgName>
          <orgName type="acronym">UT Capitole</orgName>
          <date type="start">1970-01-01</date>
          <desc>
            <address>
              <addrLine>2 rue du Doyen-Gabriel-Marty - 31042 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ut-capitole.fr/</ref>
          </desc>
          <listRelation>
            <relation name="443875" active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-443875" status="VALID">
          <idno type="ROR">https://ror.org/017tgbk05</idno>
          <orgName>Communauté d'universités et établissements de Toulouse</orgName>
          <orgName type="acronym">Comue de Toulouse</orgName>
          <desc>
            <address>
              <addrLine>41 Allée Jules Guesde, 31000 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-toulouse.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116256" status="VALID">
          <idno type="IdRef">026403994</idno>
          <idno type="ROR">https://ror.org/04ezk3x31</idno>
          <orgName>Université Toulouse - Jean Jaurès</orgName>
          <orgName type="acronym">UT2J</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>5 allées Antonio Machado - 31058 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse2.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-217752" status="OLD">
          <idno type="IdRef">026404672</idno>
          <idno type="ISNI">0000000121617331</idno>
          <idno type="ROR">https://ror.org/02v6kpv12</idno>
          <idno type="Wikidata">Q1273188</idno>
          <orgName>Université Toulouse III - Paul Sabatier</orgName>
          <orgName type="acronym">UT3</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 route de Narbonne - 31062 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse3.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-1149079" status="OLD">
          <orgName>Toulouse Mind &amp; Brain Institut</orgName>
          <orgName type="acronym">TMBI</orgName>
          <date type="start">2021-01-01</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>CHU Purpan, Pavillon Baudot, 31059 Toulouse cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.tmbi.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation name="FED4171" active="#struct-217752" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>