{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,30]],"date-time":"2025-11-30T09:08:07Z","timestamp":1764493687283,"version":"3.41.0"},"reference-count":0,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2011,11,1]],"date-time":"2011-11-01T00:00:00Z","timestamp":1320105600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2011,11]]},"abstract":"<jats:p>\n            An algorithm is described to solve multiple-phase optimal control problems using a recently developed numerical method called the\n            <jats:italic>Gauss pseudospectral method<\/jats:italic>\n            . The algorithm is well suited for use in modern vectorized programming languages such as FORTRAN 95 and MATLAB. The algorithm discretizes the cost functional and the differential-algebraic equations in each phase of the optimal control problem. The phases are then connected using linkage conditions on the state and time. A large-scale nonlinear programming problem (NLP) arises from the discretization and the significant features of the NLP are described in detail. A particular reusable MATLAB implementation of the algorithm, called\n            <jats:italic>GPOPS<\/jats:italic>\n            , is applied to three classical optimal control problems to demonstrate its utility. The algorithm described in this article will provide researchers and engineers a useful software tool and a reference when it is desired to implement the Gauss pseudospectral method in other programming languages.\n          <\/jats:p>","DOI":"10.1145\/2049662.2049671","type":"journal-article","created":{"date-parts":[[2011,12,6]],"date-time":"2011-12-06T19:05:23Z","timestamp":1323198323000},"page":"1-2","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Corrigendum"],"prefix":"10.1145","volume":"38","author":[{"given":"Anil V.","family":"Rao","sequence":"first","affiliation":[{"name":"University of Florida"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David A.","family":"Benson","sequence":"additional","affiliation":[{"name":"The Charles Stark Draper Laboratory, Inc."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christopher","family":"Darby","sequence":"additional","affiliation":[{"name":"University of Florida"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael A.","family":"Patterson","sequence":"additional","affiliation":[{"name":"University of Florida"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Camila","family":"Francolin","sequence":"additional","affiliation":[{"name":"University of Florida"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ilyssa","family":"Sanders","sequence":"additional","affiliation":[{"name":"University of Florida"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Geoffrey T.","family":"Huntington","sequence":"additional","affiliation":[{"name":"Blue Origin, LLC"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2011,12,7]]},"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2049662.2049671","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2049662.2049671","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T20:26:41Z","timestamp":1750278401000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2049662.2049671"}},"subtitle":["Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method"],"short-title":[],"issued":{"date-parts":[[2011,11]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,11]]}},"alternative-id":["10.1145\/2049662.2049671"],"URL":"https:\/\/doi.org\/10.1145\/2049662.2049671","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"type":"print","value":"0098-3500"},{"type":"electronic","value":"1557-7295"}],"subject":[],"published":{"date-parts":[[2011,11]]},"assertion":[{"value":"2011-12-07","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}