Two-Point Boundary Value Problems of Linear Hamiltonian Systems

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Previous article Next article Two-Point Boundary Value Problems of Linear Hamiltonian SystemsR. S. BucyR. S. Bucyhttps://doi.org/10.1137/0115121PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Gilbert A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Ill., 1946ix+296 MR0017881 (8,212e) 0063.00459 Google Scholar[2] Robert Hermann, On the accessibility problem in control theoryInternat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, 325–332 MR0149402 (26:6891) 0142.36102 CrossrefGoogle Scholar[3] R. E. Kalman and , R. S. Bucy, New results in linear filtering and prediction theory, Trans. ASME Ser. D. J. Basic Engrg., 83 (1961), 95–108 MR0234760 (38:3076) CrossrefGoogle Scholar[4] J. Radon, Zum Problem von Lagrange, Abh. Math. Sem. Univ. Hamburg, 6 (1928), 273–299 CrossrefGoogle Scholar[5] William T. Reid, A matrix equation related to a non-oscillation criterion and Liapunov stability, Quart. Appl. Math., 23 (1965), 83–87 MR0176997 (31:1263) 0132.00701 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Reduction of linear Hamiltonian systems of ordinary differential equations1 Jan 2015 Cross Ref Conservative numerical method for solving static linear boundary value problems of elastic shells of revolutionComputational Continuum Mechanics, Vol. 5, No. 1 | 1 Jan 2012 Cross Ref Hamiltonian approach to studying thin shells of revolution made of composite materialsJournal of Mathematical Sciences, Vol. 176, No. 5 | 6 July 2011 Cross Ref The synthesis of two suboptimal electrohydraulic suspensions, active and semiactive, employing the receding horizon methodNonlinear Analysis: Theory, Methods & Applications, Vol. 30, No. 4 | 1 Dec 1997 Cross Ref Invariant Subspace Methods for the Numerical Solution of Riccati EquationsThe Riccati Equation | 1 Jan 1991 Cross Ref Decentralized control of a class of nonlinear time‐varying interconnected systemsJournal of the Chinese Institute of Engineers, Vol. 14, No. 1 | 1 Jan 1991 Cross Ref Estimate of boundary layer thickness for linear, singularly perturbed two-point boundary-value problemsJournal of Optimization Theory and Applications, Vol. 63, No. 1 | 1 Oct 1989 Cross Ref Asymptotic solution of one class of singularly perturbed optimal control problemsJournal of Applied Mathematics and Mechanics, Vol. 47, No. 3 | 1 Jan 1983 Cross Ref Singular perturbations and optimal controlMathematical Control Theory | 26 August 2006 Cross Ref A modified quadratic cost problem and feedback stabilization of a linear systemIEEE Transactions on Automatic Control, Vol. 22, No. 5 | 1 Oct 1977 Cross Ref Singular perturbations and singular arcs--Part IIIEEE Transactions on Automatic Control, Vol. 22, No. 3 | 1 Jun 1977 Cross Ref Asymptotic Expansions of Singularly Perturbed Quasi-Linear Optimal SystemsPeddapullaiah SannutiSIAM Journal on Control, Vol. 13, No. 3 | 18 July 2006AbstractPDF (1466 KB)Singular perturbations and singular arcs--Part IIEEE Transactions on Automatic Control, Vol. 20, No. 2 | 1 Apr 1975 Cross Ref The Singularly Perturbed Linear State Regulator Problem. IIR. E. O’Malley and C. F. KungSIAM Journal on Control, Vol. 13, No. 2 | 18 July 2006AbstractPDF (854 KB)Asymptotic series solution of singularly perturbed optimal control problemsAutomatica, Vol. 10, No. 2 | 1 Mar 1974 Cross Ref An Historical Survey of Computational Methods in Optimal ControlE. PolakSIAM Review, Vol. 15, No. 2 | 2 August 2006AbstractPDF (3413 KB)Closed Loop Formulations of Optimal Control Problems for Minimum SensitivityControl and Dynamic Systems | 1 Jan 1973 Cross Ref ReferencesRiccati Differential Equations | 1 Jan 1972 Cross Ref ReferencesComputational Methods in Optimization: A Unified Approach | 1 Jan 1971 Cross Ref Solution of Ill-Conditioned linear Two-Point Boundary Value Problems by the Riccati TransformationI. H. Mufti, C. K. Chow, and F. T. StockSIAM Review, Vol. 11, No. 4 | 18 July 2006AbstractPDF (311 KB)On optimal terminal controlIEEE Transactions on Automatic Control, Vol. 14, No. 5 | 1 Oct 1969 Cross Ref Global theory of the Riccati equationJournal of Computer and System Sciences, Vol. 1, No. 4 | 1 Dec 1967 Cross Ref Volume 15, Issue 6| 1967SIAM Journal on Applied Mathematics History Submitted:14 November 1966Published online:17 February 2012 InformationCopyright © 1967 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0115121Article page range:pp. 1385-1389ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics