{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T03:11:55Z","timestamp":1787368315426,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>A new fundamental solution semigroup for operator differential Riccati equations is developed. This fundamental solution semigroup is constructed via an auxiliary finite horizon optimal control problem whose value functional growth with respect to time horizon is determined by a particular solution of the operator differential Riccati equation of interest. By exploiting semiconvexity of this value functional, and the attendant max-plus linearity and semigroup properties of the associated dynamic programming evolution operator, a semigroup of max-plus integral operators is constructed in a dual space defined via the Legendre--Fenchel transform. It is demonstrated that this semigroup of max-plus integral operators can be used to propagate all solutions of the operator differential Riccati equation that are initialized from a specified class of initial conditions. As this semigroup of max-plus integral operators can be identified with a semigroup of quadratic kernels, an explicit recipe for the aforementioned solution propagation is also rendered possible.<\/jats:p>","DOI":"10.1137\/120879312","type":"journal-article","created":{"date-parts":[[2015,4,21]],"date-time":"2015-04-21T12:28:52Z","timestamp":1429619332000},"page":"969-1002","source":"Crossref","is-referenced-by-count":14,"title":["A Max-plus Dual Space Fundamental Solution for a Class of Operator Differential Riccati Equations"],"prefix":"10.1137","volume":"53","author":[{"given":"Peter M.","family":"Dower","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William M.","family":"McEneaney","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,4,21]]},"reference":[{"key":"atypb1","first-page":"1311","volume":"11","author":"Atwell J.","year":"2001","journal-title":"Int. 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Mena,\n                      Numerical Solution of the Infinite-Dimensional LQR-Problem and the Associated Differential Riccati Equations\n                      , Preprint MPIMD\/12-13, MPI Magdeburg, 2012."},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"A. Bensoussan, G. D. Prato, M. Delfour, and S. Mitter,\n                      Representation and Control of Infinite Dimensional Systems\n                      , 2nd ed., Birkhau\u0308ser, Basel, 2007.","DOI":"10.1007\/978-0-8176-4581-6"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"R. Curtain and H. Zwart,\n                      An Introduction to Infinite-Dimensional Linear Systems Theory\n                      , Texts in Appl. 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Rockafellar,\n                      Conjugate Duality and Optimization\n                      , CBMS-NSF Conf. Ser. in Appl. Math. 16, SIAM, Philadelphia, 1974.","DOI":"10.1137\/1.9781611970524"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(91)90035-X"},{"key":"atypb22","unstructured":"A. Taylor and D. 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