Previous article Next article Synthesis of Optimal Control for an Infinite Dimensional Periodic ProblemG. Da PratoG. Da Pratohttps://doi.org/10.1137/0325039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractWe prove an existence and uniqueness result on periodic solutions of an infinite dimensional Riccati equation.[1] V. Barbu and , G. Da Prato, Hamilton-Jacobi Equations in Hilbert Spaces, Pitman, London, 1983 0508.34001 Google Scholar[2] S. Bittanti, , A. Locatelli and , C. Maffezzoni, A. Marzollo, Periodic optimization under small perturbationsPeriodic Optimization, Vol. II, Udine, Springer-Verlag, Berlin, New York, 1972, 183–231 0286.49021 Google Scholar[3] R. F. Curtain and , A. J. Pritchard, Infinite Dimensional Linear Systems, Springer-Verlag, Berlin, New York, 1980 Google Scholar[4] 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[5] R. E. Kalman, , P. L. Falb and , M. A. Arbib, Topics in Mathematical System Theory, McGraw-Hill, New York, 1960 Google Scholar[6] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, Vol. 44, Springer-Verlag, New York, 1983viii+279, Berlin 85g:47061 0516.47023 CrossrefGoogle Scholar[7] A. J. Pritchard and , J. Zabczyk, Stability and stabilizability of infinite-dimensional systems, SIAM Rev., 23 (1981), 25–52 10.1137/1023003 82f:93063 0452.93029 LinkISIGoogle Scholar[8] 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[9] 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 ScholarKeywordsoptimal controlperiodic controldynamic programming Previous article Next article FiguresRelatedReferencesCited byDetails Assignment of the upper Bohl exponent for linear periodic control systems in Hilbert spacesEuropean Journal of Control, Vol. 67 Cross Ref Local feedback stabilization of time-periodic evolution equations by finite dimensional controls10 December 2020 | ESAIM: Control, Optimisation and Calculus of Variations, Vol. 26 Cross Ref Linear Stochastic Differential Equations Driven by Gauss-Volterra Processes and Related Linear-Quadratic Control Problems22 December 2017 | Applied Mathematics & Optimization, Vol. 80, No. 2 Cross Ref Mathematical Machinery12 November 2016 Cross Ref Applications to Stochastic Optimal Control12 November 2016 Cross Ref References5 June 2012 Cross Ref Nonlinear Optimal Control Techniques for Vibration Attenuation Using Magnetostrictive Actuators29 March 2007 | Journal of Intelligent Material Systems and Structures, Vol. 19, No. 2 Cross Ref Output regulation of time-varying systemsSystems & Control Letters, Vol. 55, No. 12 Cross Ref Synthesis of finite-dimensional riccati-based feedback controls for problems arising in structural acousticsJournal of the Franklin Institute, Vol. 336, No. 4 Cross Ref A Nonlinear Optimal Control Method for Magnetostrictive Actuators27 July 2016 | Journal of Intelligent Material Systems and Structures, Vol. 9, No. 6 Cross Ref LQR Control of Thin Shell Dynamics: Formulation and Numerical Implementation27 July 2016 | Journal of Intelligent Material Systems and Structures, Vol. 9, No. 4 Cross Ref LQR Control of Shell Vibrations via Piezoceramic Actuators Cross Ref Optimal Control of Linear Periodic Resonant Systems in Hilbert SpacesViorel Barbu26 July 2006 | SIAM Journal on Control and Optimization, Vol. 35, No. 6AbstractPDF (654 KB)Experimental Confirmation of a PDE-Based Approach to Design of Feedback ControlsH. 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