Riccati Equation Arising in a Boundary Control Problem with Distributed Parameters

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Previous article Next article Riccati Equation Arising in a Boundary Control Problem with Distributed ParametersFranco FlandoliFranco Flandolihttps://doi.org/10.1137/0322006PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractGlobal existence is proved for the solution, of a Riccati differential equation connected with the synthesis of a boundary control problem governed by parabolic partial differential equations.[1] A. V. Balakrishnan, Boundary control of parabolic equations: L−Q−R theoryTheory of nonlinear operators (Proc. Fifth Internat. Summer School, Central Inst. Math. Mech. Acad. Sci. GDR, Berlin, 1977), Abh. Akad. Wiss. DDR, Abt. Math. Naturwiss. Tech., 1978, Vol. 6, Akademie-Verlag, Berlin, 1978, 11–23 80j:93058 0427.49005 Google Scholar[2] R. Curtain and , A. Pritchard, Infinite dimensional linear systems theory, Lecture Notes in Control and Information Sciences, Vol. 8, Springer-Verlag, Berlin, 1978vii+297 80h:93002 0389.93001 CrossrefGoogle Scholar[3] G. Da Prato, Quelques résultats d'existence, unicité et régularité pour un problème de la théorie du contrôle, J. Math. Pures Appl. (9), 52 (1973), 353–375 (1974) 50:10896 0289.93027 Google Scholar[4] Franco Flandoli, Riccati equation arising in a stochastic optimal control problem with boundary control, Boll. Un. Mat. Ital. C (6), 1 (1982), 377–393 85a:93165 0512.49007 Google Scholar[5] G. H. Hardy, , J. E. Littlewood and , G. Polya, Inequalities, Cambridge University Press, Cambridge, 1934, 290– 0010.10703 Google Scholar[6] Irena Lasiecka, Unified theory for abstract parabolic boundary problems—a semigroup approach, Appl. Math. Optim., 6 (1980), 287–333 81m:35077 0448.47019 CrossrefISIGoogle Scholar[7] J. L. Lions, Optimal control of systems governed by partial differential equations, Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, Band 170, Springer-Verlag, New York, 1971xi+396 42:6395 0203.09001 CrossrefGoogle Scholar[8] J. L. Lions and , J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math., (1964), 5–68, Paris 29:2627 0148.11403 CrossrefGoogle Scholar[9] M. Sorine, Une resultat d'existence et unicité pour l'équation de Riccati stationnaire, Rapport INRIA, 55, 1981 Google Scholar[10] M. Sorine, Sur le semigroupe non linéaire associé à l'equation de Riccati, Rapport du CRMA, 1055, Université de Montréal, 1981 Google Scholar[11] Hiroki Tanabe, Equations of evolution, Monographs and Studies in Mathematics, Vol. 6, Pitman (Advanced Publishing Program), Boston, Mass., 1979xii+260 82g:47032 0417.35003 Google Scholar[12] Luc Tartar, Sur l'étude directe d'équations non linéaires intervenant en théorie du contrôle optimal, J. Functional Analysis, 17 (1974), 1–47 50:14406 0293.49004 CrossrefGoogle ScholarKeywordsRiccati equationoptimal controlparabolic systemsDirichlet boundary control Previous article Next article FiguresRelatedReferencesCited byDetails Finite-Horizon Parameterizing Manifolds, and Applications to Suboptimal Control of Nonlinear Parabolic PDEs26 September 2014 | Acta Applicandae Mathematicae, Vol. 135, No. 1 Cross Ref Riccati equations for generalized singular estimate control systemsApplicable Analysis, Vol. 92, No. 8 Cross Ref RICCATI EQUATION IN QUADRATIC OPTIMAL CONTROL PROBLEM OF DAMPED SECOND ORDER SYSTEMJournal of the Korean Mathematical Society, Vol. 50, No. 1 Cross Ref Riccati theory and singular estimates for a Bolza control problem arising in linearized fluid–structure interactionSystems & Control Letters, Vol. 58, No. 7 Cross Ref Optimal Feedback Synthesis for Bolza Control Problem Arising in Linearized Fluid Structure Interaction2 December 2009 Cross Ref Kalman-Popov-Yakubovich lemma and the S-procedure: A historical essayAutomation and Remote Control, Vol. 67, No. 11 Cross Ref Discussion on: “Boundary Control of a Class of Hyperbolic Systems”European Journal of Control, Vol. 9, No. 6 Cross Ref An Infinite Horizon Linear Quadratic Problem with Unbounded Controls in Hilbert SpaceActa Mathematica Sinica, English Series, Vol. 17, No. 3 Cross Ref Second Order Hamilton--Jacobi Equations in Hilbert Spaces and Stochastic Boundary ControlFausto Gozzi, Elisabeth Rouy, and Andrzej Swiech26 July 2006 | SIAM Journal on Control and Optimization, Vol. 38, No. 2AbstractPDF (503 KB)Partially stabilizing LQ-optimal control for stabilizable semigroup systemsIntegral Equations and Operator Theory, Vol. 32, No. 2 Cross Ref Infinite-Dimensional Hamilton–Jacobi Equations and Dirichlet Boundary Control Problems of Parabolic TypePiermarco Cannarsa and Maria Elisabetta Tessitore17 February 2012 | SIAM Journal on Control and Optimization, Vol. 34, No. 6AbstractPDF (1377 KB)Input dynamics and nonstandard riccati equations with applications to boundary control of damped wave and plate equationsJournal of Optimization Theory and Applications, Vol. 84, No. 3 Cross Ref Finite Element Approximations of Compensator Design for Analytic Generators with Fully Unbounded Controls/ObservationsI. 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