Controllability and the Singular Problem

Abstract

Previous article Next article Controllability and the Singular ProblemH. HermesH. Hermeshttps://doi.org/10.1137/0302022PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. E. Kalman, Contributions to the theory of optimal control, Bol. Soc. Mat. Mexicana (2), 5 (1960), 102–119 MR0127472 0112.06303 Google Scholar[2] H. Hermes and , G. Haynes, On the nonlinear control problem with control appearing linearly, J. Soc. Indust. Appl. Math. Ser. A Control, 1 (1963), 85–108 (1963) MR0170738 0145.12602 LinkGoogle Scholar[3] C. Carathéodory, Untersuchungen über die Grundlagen der Thermodynamik, Math. Ann., 67 (1909), 355–386 MR1511534 CrossrefGoogle Scholar[4] W. L. Chow, Über Systeme von linear partiellen Differentialgleiehungen erster Ordnung, Math. Ann., (1940), 95–105 Google Scholar[5] J. P. LaSalle, The time optimal control problemContributions to the theory of nonlinear oscillations, Vol. V, Princeton Univ. Press, Princeton, N.J., 1960, 1–24 MR0145169 Google Scholar[6] R. E. Kalman, , Y. C. Ho and , K. S. Narendra, Controllability of linear dynamical systems, Contributions to Differential Equations, 1 (1963), 189–213 MR0155070 0151.13303 Google Scholar[7] Earl A. Coddington and , Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955xii+429 MR0069338 0064.33002 Google Scholar[8] J. Milnor, Morse theory, Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963vi+153 MR0163331 0108.10401 CrossrefGoogle Scholar[9] E. B. Lee and , L. Markus, Optimal control for nonlinear processes, Arch. Rational Mech. Anal., 8 (1961), 36–58 MR0128571 0099.08703 CrossrefISIGoogle Scholar[10] R. E. Kalman, Discussion of Optimal control for nonlinear processes, Trans. ASME Ser. D. J. Basic Engrg., 84 (1962), Google Scholar[11] L. S. Pontryagin, , V. G. Boltyanskii, , R. V. Gamkrelidze and , E. F. Mishchenko, The mathematical theory of optimal processes, Translated from the Russian by K. N. Trirogoff; edited by L. W. Neustadt, Interscience Publishers John Wiley & Sons, Inc. New York-London, 1962viii+360 MR0166037 0102.32001 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Controlling Nonlinear Infinite-Dimensional Systems via the Initial StateNeil D. Evans3 October 2013 | SIAM Journal on Control and Optimization, Vol. 51, No. 5AbstractPDF (294 KB)A Characterization of the Reachable Set for Nonlinear Control SystemsRichard Vinter18 July 2006 | SIAM Journal on Control and Optimization, Vol. 18, No. 6AbstractPDF (1184 KB)On the Set of Attainability of Nonlinear Nonautonomous Control SystemsD. Rebhuhn1 August 2006 | SIAM Journal on Control and Optimization, Vol. 15, No. 5AbstractPDF (1054 KB)Global Bilinearization of Systems with Control Appearing LinearlyJames Ting-Ho Lo18 July 2006 | SIAM Journal on Control, Vol. 13, No. 4AbstractPDF (511 KB)On Local and Global ControllabilityH. Hermes18 July 2006 | SIAM Journal on Control, Vol. 12, No. 2AbstractPDF (1057 KB)A Generalization of Chow’s Theorem and the Bang-Bang Theorem to Nonlinear Control ProblemsArthur J. Krener18 July 2006 | SIAM Journal on Control, Vol. 12, No. 1AbstractPDF (893 KB)The Geometry of Time-Optimal ControlHenry Hermes18 July 2006 | SIAM Journal on Control, Vol. 10, No. 2AbstractPDF (934 KB)Controllability, Realization and Stability of Discrete-Time SystemsLeonard Weiss18 July 2006 | SIAM Journal on Control, Vol. 10, No. 2AbstractPDF (1937 KB)Global Controllability of Nonlinear SystemsD. L. Lukes18 July 2006 | SIAM Journal on Control, Vol. 10, No. 1AbstractPDF (1137 KB)Some Sufficient Conditions for the Global and Local Controllability of Nonlinear Time-Varying SystemsE. J. Davison and E. G. Kunze18 July 2006 | SIAM Journal on Control, Vol. 8, No. 4AbstractPDF (725 KB)Contrôlabilité des Systèmes non LinéairesClaude Lobry18 July 2006 | SIAM Journal on Control, Vol. 8, No. 4AbstractPDF (64421 KB)Sufficient Conditions for Nonnegativity of the Second Variation in Singular and Nonsingular Control ProblemsD. H. Jacobson18 July 2006 | SIAM Journal on Control, Vol. 8, No. 3AbstractPDF (1488 KB)A New Necessary Condition of Optimality for Singular Control ProblemsD. H. Jacobson1 August 2006 | SIAM Journal on Control, Vol. 7, No. 4AbstractPDF (1341 KB)Invariant Subspaces and the Controllability and Observability of Linear Dynamical SystemsD. A. Ford and C. D. Johnson18 July 2006 | SIAM Journal on Control, Vol. 6, No. 4AbstractPDF (693 KB)On the Optimality of a Totally Singular Vector Control: An Extension of the Green’s Theorem Approach to Higher DimensionsGeorge W. Haynes18 July 2006 | SIAM Journal on Control, Vol. 4, No. 4AbstractPDF (1279 KB) Volume 2, Issue 2| 1964Journal of the Society for Industrial and Applied Mathematics Series A Control History Submitted:12 November 1964Published online:18 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0302022Article page range:pp. 241-260ISSN (print):0887-4603ISSN (online):2168-359XPublisher:Society for Industrial and Applied Mathematics