{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:43:16Z","timestamp":1787319796698,"version":"build-2736575974"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>Let G be a Lie group. In order to study optimal control problems on a homogeneous space $G\/H$, we identify its cotangent bundle $T^{\\ast}G\/H$ as a subbundle of the cotangent bundle of G. Next, this identification is used to describe the Hamiltonian lifting of vector fields on $G\/H$ induced by elements in the Lie algebra $\\mathfrak{g}$ of G. As an application, we consider a bilinear control system $\\Sigma$ in $\\mathbb{R}^{2}$ whose matrices generate $\\mathfrak{s}l(2)$. Through the Pontryagin maximum principle, we analyze the time-optimal problem for the angle system $\\mathbb{P}\\Sigma$ defined by the projection of $\\Sigma$ onto the projective line $\\mathbb{P}^{1}$. We compute some examples, and in particular we show that the bang-bang principle does not need to be true.<\/jats:p>","DOI":"10.1137\/080736867","type":"journal-article","created":{"date-parts":[[2009,9,4]],"date-time":"2009-09-04T18:16:11Z","timestamp":1252088171000},"page":"2636-2650","source":"Crossref","is-referenced-by-count":3,"title":["Optimality on Homogeneous Spaces, and the Angle System Associated with a Bilinear Control System"],"prefix":"10.1137","volume":"48","author":[{"given":"V.","family":"Ayala","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. C.","family":"Rodr\u00edguez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L. A. B. San","family":"Martin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,9,4]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.22199\/S07160917.1999.0002.00008"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013003204923"},{"key":"R3","unstructured":"U. Boscain and B. Piccoli,\n                      Optimal synthesis for control systems on 2-D manifolds\n                      , Math. Appl. (Berlin), 43, Springer, Berlin, 2004."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.22199\/S07160917.1996.0002.00002"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"F. Colonius and W. Kliemann,\n                      Dynamics and Control\n                      , Birkh\u00e4user, Cambridge, MA, 1999.","DOI":"10.1007\/978-1-4612-1350-5"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"V. Jurdjevic,\n                      Geometric Control Theory\n                      , Cambridge University Press, New York, 1997.","DOI":"10.1017\/CBO9780511530036"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-247X(02)00008-2"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-000-0002-8"},{"key":"R9","unstructured":"A. Sagle and R. Walde,\n                      Introduction to Lie Groups and Lie Algebras\n                      , Academic Press, New York and London, 1973."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573505"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01213469"},{"key":"R12","first-page":"1","volume":"27","author":"Sussmann H.","year":"1982","journal-title":"Progress in Mathematics, Differential Geometric Control Theory, Proceedings of the conference held at Michigan Technological University"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/0325048"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/0325062"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080736867","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:52:19Z","timestamp":1787316739000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080736867"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/080736867"],"URL":"https:\/\/doi.org\/10.1137\/080736867","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}