On The Nonlinear Control Problem with Control Appearing Linearly

Next article On The Nonlinear Control Problem with Control Appearing LinearlyH. Hermes and G. HaynesH. Hermes and G. Hayneshttps://doi.org/10.1137/0301007PDFBibTexSections 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 0063.00459 Google Scholar[2] V. G. Boltyanskii, , R. V. Gamkrelidze and , L. S. Pontryagin, Optimal control processes, Uspelhi Mat. Nauk., 14 (1959), 3–20 Google Scholar[3] 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[4] A. F. Filippov, On certain questions in the theory of optimal control, J. SIAM Control Ser. A, 1 (1962), 76–84, (English Translation.) 10.1137/0301006 MR0149985 0139.05102 LinkGoogle Scholar[5] R. E. Kalman, The theory of optimal control and the calculus of variations, RIAS Technical Report, 6-13, Research Institute for Advanced Studies (RIAS), Baltimore, 1961 Google Scholar[6] 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[7] D. F. Lawden, Optimal powered arcs in an inverse square law field, J. Amer. Rocket. Soc., 31 (1961), 566–568 Google Scholar[8] E. B. Lee, Time optimal control of nonlinear processes, Presented to J.A.C.C., Trans. A.S.M.E., Paper No. 61-JAC-3, Boulder, Colo., 1961 Google Scholar[9] D. L. Lukes, Steepest Descent and Maximum Principle Techniques of System Optimization, Symposium on Vehicle Systems Optimization, Garden City, L. I., New York, 1961, 36–41 Google Scholar[10] E. B. Lee and , L. Markus, Optimal control for nonlinear processes, Arch. Rational Mech. Anal., 8 (1961), 36–58 MR0128571 0099.08703 CrossrefISIGoogle Scholar[11] A. Miele, Application of Green's Theorem to the Extremization of Linear Integrals, Symposium On Vehicle Systems Optimization, Garden City, L. I., New York, 1961, 26–35 Google Scholar[12] I. P. Natanson, Theory of functions of a real variable, Frederick Ungar Publishing Co., New York, 1955, 277–, Vol. I MR0067952 0064.29102 Google Scholar[13] M. H. A. Newman, Elements of the Topology of Plane Sets of Points, Cambridge University Press, Princeton, 1954 Google Scholar[14] E. Roxin, A geometric interpretation of Pontryagin's maximum principle, RIAS Technical Report, 61-15, Research Institute for Advanced Studies (RIAS), Baltimore, 1961 Google Scholar[15] Emilio Roxin, The existence of optimal controls, Michigan Math. J., 9 (1962), 109–119 10.1307/mmj/1028998668 MR0136844 0105.07801 CrossrefGoogle Scholar Next article FiguresRelatedReferencesCited byDetails Rates of Convergence for Conditional Gradient Algorithms Near Singular and Nonsingular ExtremalsJ. C. Dunn18 July 2006 | SIAM Journal on Control and Optimization, Vol. 17, No. 2AbstractPDF (2252 KB)Dynamic Optimal Control Models in Advertising: a SurveySuresh P. Sethi17 February 2012 | SIAM Review, Vol. 19, No. 4AbstractPDF (4271 KB)Global Bilinearization of Systems with Control Appearing LinearlyJames Ting-Ho Lo18 July 2006 | SIAM Journal on Control, Vol. 13, No. 4AbstractPDF (511 KB)High Order Necessary Conditions for OptimalityR. Gabasov and F. M. Kirillova18 July 2006 | SIAM Journal on Control, Vol. 10, No. 1AbstractPDF (3556 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)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)Controllability and the Singular ProblemH. Hermes18 July 2006 | Journal of the Society for Industrial and Applied Mathematics Series A Control, Vol. 2, No. 2AbstractPDF (1775 KB) Volume 1, Issue 2| 1963Journal of the Society for Industrial and Applied Mathematics Series A Control History Submitted:27 October 1962Published online:18 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0301007Article page range:pp. 85-108ISSN (print):0887-4603ISSN (online):2168-359XPublisher:Society for Industrial and Applied Mathematics