An Iterative Procedure for Solving the Time-Optimal Regulator Problem

Next article An Iterative Procedure for Solving the Time-Optimal Regulator ProblemToshio Fujisawa and Yutaka YasudaToshio Fujisawa and Yutaka Yasudahttps://doi.org/10.1137/0305029PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] 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[2] 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[3] Lucien W. Neustadt, Synthesizing time optimal control systems, J. Math. Anal. Appl., 1 (1960), 484–493 10.1016/0022-247X(60)90015-9 MR0128573 0100.09903 CrossrefGoogle Scholar[4] J. H. Eaton, An iterative solution to time-optimal control, J. Math. Anal. Appl., 5 (1962), 329–344 10.1016/S0022-247X(62)80015-8 MR0140800 0142.06801 CrossrefGoogle Scholar[5] B. N. Psenicnyi˘, A numerical method for computing the time-optimal control in linear systems, Z. Vycisl. Mat. i Mat. Fiz., 4 (1964), 52–60 MR0163801 Google Scholar[6] T. G. Babunashvili, The synthesis of linear optimal systems, J. Soc. Indust. Appl. Math. Ser. A Control, 2 (1964), 261–265 MR0176870 0139.05001 LinkGoogle Scholar[7] V. F. Dem'janov, Construction of an optimum program in a linear system, Avtomat. i Telemeh., 25 (1964), 3–11 MR0189874 Google Scholar[8] Edward J. Fadden and , Elmer G. Gilbert, A. V. Balakrishnan and , L. W. Neustadt, Computational aspects of the time-optimal control problemComputing Methods in Optimization Problems (Proc. Conf., Univ. California, Los Angeles, Calif., 1964), Academic Press, New York, 1964, 167–192 MR0168413 0161.07103 CrossrefGoogle Scholar[9] Robert O. Barr, Computation of optimal controls on convex reachable setsMathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967), Academic Press, New York, 1967, 63–70 MR0252071 0223.65027 Google Scholar[10] Robert O. Barr and , Elmer G. Gilbert, Some iterative procedures for computing optimal controlsAutomatic and remote control III (Proc. Third Congr. Internat. Federation Automat. Control (IFAC), London, 1966), Vol. 1, p. 47, Paper 24D, Inst. Mech. Engrs., London, 1967, 9– MR0378410 Google Scholar[11] Marguerite Frank and , Philip Wolfe, An algorithm for quadratic programming, Naval Res. Logist. Quart., 3 (1956), 95–110 MR0089102 CrossrefGoogle Scholar[12] Claude Berge and , A. Ghouila-Houri, Programming, games and transportation networks, Translated from the French by Maxine Merrington and C. Ramanujacharyulu, Methuen and Co., Ltd., London, 1965x+260 MR0198964 0138.15505 Google Scholar[13] Paul Strimple Fancher, Iterative computation procedures for an optimum control problem, IEEE Trans. Automatic Control, AC-10 (1965), 346–348 10.1109/TAC.1965.1098170 MR0186443 CrossrefISIGoogle Scholar[14] Elmer G. Gilbert, An iterative procedure for computing the minimum of a quadratic form on a convex set, SIAM J. Control, 4 (1966), 61–80 10.1137/0304007 MR0189875 0196.51204 LinkGoogle Scholar Next article FiguresRelatedReferencesCited byDetails An Approximation Scheme for the Minimum Time FunctionM. Bardi and M. Falcone1 August 2006 | SIAM Journal on Control and Optimization, Vol. 28, No. 4AbstractPDF (1664 KB)Accelerated Frank–Wolfe AlgorithmsGerard G. L. Meyer1 August 2006 | SIAM Journal on Control, Vol. 12, No. 4AbstractPDF (877 KB)An Efficient Computational Procedure for a Generalized Quadratic Programming ProblemRobert O. Barr18 July 2006 | SIAM Journal on Control, Vol. 7, No. 3AbstractPDF (1516 KB) Volume 5, Issue 4| 1967SIAM Journal on Control History Submitted:12 August 1966Published online:18 July 2006 InformationCopyright © 1967 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0305029Article page range:pp. 501-512ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics