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We show that the control-to-state mapping is differentiable in a certain generalized sense, which implies Fr\u00e9chet-differentiability with respect to the control functions and the switching points for the composition with a tracking type functional, even in the presence of shocks. We also present an adjoint-based formula for the gradient of the reduced objective functional.<\/jats:p>","DOI":"10.1137\/140995799","type":"journal-article","created":{"date-parts":[[2015,5,14]],"date-time":"2015-05-14T12:09:56Z","timestamp":1431605396000},"page":"1250-1277","source":"Crossref","is-referenced-by-count":14,"title":["Optimal Boundary Control of Nonlinear Hyperbolic Conservation Laws with Switched Boundary Data"],"prefix":"10.1137","volume":"53","author":[{"given":"Sebastian","family":"Pfaff","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"Ulbrich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,5,14]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012902407776"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012996304407"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1080\/03605307908820117"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2000.6.329"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(97)00536-1"},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"A. Bressan,\n                      Hyperbolic Systems of Conservation Laws\n                      : The One-Dimensional Cauchy Problem, Oxford Lecture Ser. Math. Appl. 20, Oxford University Press, Oxford, UK, 2000.","DOI":"10.1093\/oso\/9780198507000.001.0001"},{"key":"atypb7","doi-asserted-by":"crossref","first-page":"35","DOI":"10.3934\/dcds.1997.3.35","volume":"3","author":"Bressan A.","year":"1997","journal-title":"Discrete Contin. Dyn. 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Ulbrich,\n                      Optimal Control of Nonlinear Hyperbolic Conservation Laws with Source Terms\n                      , Habilitation, Zentrum Mathematik, Technische Universita\u0308t Mu\u0308nchen, Germany, 2001."},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900370764"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(02)00275-X"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1007\/s002050100157"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/140995799","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:22:08Z","timestamp":1787322128000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/140995799"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":33,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/140995799"],"URL":"https:\/\/doi.org\/10.1137\/140995799","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}