{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T06:08:28Z","timestamp":1781762908780,"version":"3.54.5"},"reference-count":27,"publisher":"University of Szeged","issue":"4","license":[{"start":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T00:00:00Z","timestamp":1711929600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100018833","name":"Agence de l'innovation de D\u00e9fense","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100018833","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Acta Cybern"],"abstract":"<jats:p>This paper presents a constraint-based approach to compute the reachable tube of nonlinear differentiable equations. A set of initial values for the equations is considered and defined by a polytope represented as intersections of zonotopes. Guaranteed numerical integration based on zonotopic computation is used to compute reachable tubes. In order to efficiently build polytopes defined by the intersection of several zonotopes, we use a previously developed abstract domain to represent reachable tubes. The proposed contribution allows to compute more expressive reachable tubes more efficiently than methods based only on boxes, and therefore could improve verification\/validation processes in robotics application for example. The approach is evaluated on examples taken from literature and we present two applications of this work.<\/jats:p>","DOI":"10.14232\/actacyb.3007711","type":"journal-article","created":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T03:47:24Z","timestamp":1733197644000},"page":"755-774","source":"Crossref","is-referenced-by-count":1,"title":["A Constraint Programming Approach for Polytopic Simulation of Ordinary Differential Equations"],"prefix":"10.14232","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6185-2480","authenticated-orcid":false,"given":"Julien","family":"Alexandre dit Sandretto","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0309cs235","id-type":"ROR","asserted-by":"publisher"}],"name":"ENSTA Paris, Institut Polytechnique de Paris"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7230-0710","authenticated-orcid":false,"given":"Alexandre","family":"Chapoutot","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0309cs235","id-type":"ROR","asserted-by":"publisher"}],"name":"ENSTA Paris, Institut Polytechnique de Paris"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4467-2939","authenticated-orcid":false,"given":"Christophe","family":"Garion","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04gyj6s21","id-type":"ROR","asserted-by":"publisher"}],"name":"ISAE-SUPAERO"},{"id":[{"id":"https:\/\/ror.org\/004raaa70","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e9 de Toulouse"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-1126-6835","authenticated-orcid":false,"given":"Xavier","family":"Thirioux","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04gyj6s21","id-type":"ROR","asserted-by":"publisher"}],"name":"ISAE-SUPAERO"},{"id":[{"id":"https:\/\/ror.org\/004raaa70","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e9 de Toulouse"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"5401","published-online":{"date-parts":[[2024,4,1]]},"reference":[{"key":"ref1","first-page":"79","article-title":"Validated explicit and implicit Runge-Kutta methods","volume":"22","author":"Alexandre dit Sandretto","year":"2016","unstructured":"Alexandre dit Sandretto, J. and Chapoutot, A. Validated explicit and implicit Runge-Kutta methods. Reliable Computing, 22(1):79-103, 2016.","journal-title":"Reliable Computing"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/CDC45484.2021.9683622"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-98935-8_2"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-00250-3_1"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.29007\/zbkv"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-control-071420-081941"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2011.6160872"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1145\/361002.361007"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02658-4_46"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.5555\/1787526.1787534"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1002\/9781119121534"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1002\/anac.200310012"},{"key":"ref13","volume-title":"Self-Validated Numerical Methods and Applications","author":"de Figueiredo","year":"1997","unstructured":"de Figueiredo, L.H. and Stolfi, J. Self-Validated Numerical Methods and Applications. Brazilian Math. Colloquium monographs. IMPA\/CNPq, 1997."},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s10270-012-0295-3"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14295-6_22"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.5555\/1886008.1886031"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-46430-1_14"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-48085-3_18"},{"key":"ref19","volume-title":"Interval Analysis","author":"Moore","year":"1966","unstructured":"Moore, R.E. Interval Analysis. Prentice Hall, 1966.","ISSN":"https:\/\/id.crossref.org\/issn\/2577-9435","issn-type":"print"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(98)10083-8"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35873-9_26"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-58475-7_32"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s002080010018"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2018.2816262"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1145\/1186954.1187085"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2015.7403181"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1145\/3427762.3429453"}],"container-title":["Acta Cybernetica"],"original-title":[],"link":[{"URL":"https:\/\/cyber.bibl.u-szeged.hu\/index.php\/actcybern\/article\/download\/4359\/4101","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/cyber.bibl.u-szeged.hu\/index.php\/actcybern\/article\/download\/4359\/4101","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T03:47:27Z","timestamp":1733197647000},"score":1,"resource":{"primary":{"URL":"https:\/\/cyber.bibl.u-szeged.hu\/index.php\/actcybern\/article\/view\/4359"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,1]]},"references-count":27,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,11,26]]}},"URL":"https:\/\/doi.org\/10.14232\/actacyb.3007711","relation":{},"ISSN":["2676-993X","0324-721X"],"issn-type":[{"value":"2676-993X","type":"electronic"},{"value":"0324-721X","type":"print"}],"subject":[],"published":{"date-parts":[[2024,4,1]]}}}