Necessary Conditions for Control Problems with Variable Time Lags

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Previous article Next article Necessary Conditions for Control Problems with Variable Time LagsH. T. BanksH. T. Bankshttps://doi.org/10.1137/0306002PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. V. Gamkrelidze, On some extremal problems in the theory of differential equations with applications to the theory of optimal control, J. Soc. Indust. Appl. Math. Ser. A Control, 3 (1965), 106–128 MR0192937 0296.49009 LinkGoogle Scholar[2] Lucien W. Neustadt, An abstract variational theory with applications to a broad class of optimization problems. I. General theory, SIAM J. Control, 4 (1966), 505–527 10.1137/0304040 MR0216349 0166.09401 LinkGoogle Scholar[3] Avner Friedman, Optimal control for hereditary processes, Arch. Rational Mech. Anal., 15 (1964), 396–416 10.1007/BF00256929 MR0170744 0122.10801 CrossrefISIGoogle Scholar[4] M. Namı k Oğuztöreli, Time-lag control systems, Mathematics in Science and Engineering, Vol. 24, Academic Press, New York, 1966xii+323 MR0217394 0143.12101 Google Scholar[5] 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[6] Nelson Dunford and , Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York, 1958xiv+858 MR0117523 0084.10402 Google Scholar[7] Edward James McShane, Integration, Princeton University Press, Princeton, N. J., 1944 1957viii+394 pp. (Fourth printing 1957) MR0082536 0060.13010 Google Scholar[8] I. P. Natanson, Theory of functions of a real variable, Frederick Ungar Publishing Co., New York, 1955, 277– MR0067952 0064.29102 Google Scholar[9] V. Volterra, Theory of Functionals, Blackie, London, 1930 Google Scholar[10] Serge Lang, Introduction to differentiable manifolds, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962x+126 MR0155257 0103.15101 Google Scholar[11] Richard Bellman and , Kenneth L. Cooke, Differential-difference equations, Academic Press, New York, 1963xvi+462 MR0147745 0105.06402 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Viscosity Solutions of Hamilton--Jacobi--Bellman--Isaacs Equations for Time-Delay SystemsAnton PlaksinSIAM Journal on Control and Optimization, Vol. 59, No. 3 | 27 May 2021AbstractPDF (545 KB)Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal ControlRiccardo Bonalli, Bruno Hérissé, and Emmanuel TrélatSIAM Journal on Control and Optimization, Vol. 57, No. 2 | 18 April 2019AbstractPDF (576 KB)The Instability of Optimal Control Problems to Time DelaySIAM Journal on Control and Optimization, Vol. 43, No. 5 | 26 July 2006AbstractPDF (340 KB)The Sensitivity of Optimal Control Problems to Time DelaySIAM Journal on Control and Optimization, Vol. 29, No. 5 | 1 August 2006AbstractPDF (3904 KB)The Euclidean Space Controllability of Control Systems with DelaySIAM Journal on Control, Vol. 12, No. 4 | 1 August 2006AbstractPDF (1170 KB)Optimal Controls with PseudodelaysSIAM Journal on Control, Vol. 12, No. 2 | 18 July 2006AbstractPDF (1227 KB)Control of Functional Differential Equations of Retarded and Neutral Type to Target Sets in Function SpaceSIAM Journal on Control, Vol. 10, No. 4 | 18 July 2006AbstractPDF (2496 KB)The Optimization of Trajectories of Linear Functional Differential EquationsSIAM Journal on Control, Vol. 8, No. 4 | 18 July 2006AbstractPDF (2777 KB)Variational Problems Involving Functional Differential EquationsSIAM Journal on Control, Vol. 7, No. 1 | 18 July 2006AbstractPDF (1431 KB) Volume 6, Issue 1| 1968SIAM Journal on Control1-147 History Submitted:30 June 1967Published online:18 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0306002Article page range:pp. 9-47ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics