Principle For Optimal Control Problems Research Articles

A maximum principle for optimal control problems with neutral functional differential systems

A maximum principle for optimal control problems with neutral functional differential systems

A maximum principle for optimal control problems with functional differential systems

Maximum principle in integral form for optimal control problems with delay differential system equations, using vector matrix notation

Optimal Controls for Systems with Time Lag

Previous article Next article Optimal Controls for Systems with Time LagA. HalanayA. Halanayhttps://doi.org/10.1137/0306016PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. L. Kharatishvili, The maximum principle in the theory of optimal processes with time lag, Dokl. Akad. Nauk SSSR, 136 (1961), 39–42 Google Scholar[1A] 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[2] Avner Friedman, Optimal control for hereditary processes, Arch. Rational Mech. Anal., 15 (1964), 396–416 10.1007/BF00256929 MR0170744 0122.10801 CrossrefISIGoogle Scholar[3] I. A. Oziganova, On the theory of optimal control of systems with time lag, Seminar on Differential Equations with Deviating Arguments, Vol. II, University of the Friendship of Peoples, Moscow, 1963, 136–145, See also: On the theory of optimal control for problems with time lag, thesis, University of the Friendship of Peoples, Moscow, 1966. Google Scholar[4] Magnus R. Hestenes, On variational theory and optimal control theory, J. Soc. Indust. Appl. Math. Ser. A Control, 3 (1965), 23–48 MR0184763 0151.12803 LinkGoogle Scholar[5] Rodney D. Driver, Existence and stability of solutions of a delay-differential system, Arch. Rational Mech. Anal., 10 (1962), 401–426 10.1007/BF00281203 MR0141863 0105.30401 CrossrefISIGoogle Scholar[6] 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[7] G. L. Kharatishvili, A. V. Balakrishnan and , L. W. Neustadt, A maximum principle in extremal problems with delaysMathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967), Academic Press, New York, 1967, 26–34 MR0256240 0216.17701 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal ControlRiccardo Bonalli, Bruno Hérissé, and Emmanuel Trélat18 April 2019 | SIAM Journal on Control and Optimization, Vol. 57, No. 2AbstractPDF (576 KB)Optimal Control Problems with Time Delays: Constancy of the HamiltonianRichard B. Vinter25 July 2019 | SIAM Journal on Control and Optimization, Vol. 57, No. 4AbstractPDF (525 KB)The Maximum Principle for Optimal Control Problems with Time DelaysA. Boccia and R. B. Vinter19 September 2017 | SIAM Journal on Control and Optimization, Vol. 55, No. 5AbstractPDF (407 KB)The Construction of the Solution of an Optimal Control Problem Described by a Volterra Integral Equation17 February 2012 | SIAM Journal on Control and Optimization, Vol. 21, No. 4AbstractPDF (1468 KB)Optimal Controls with Pseudodelays18 July 2006 | SIAM Journal on Control, Vol. 12, No. 2AbstractPDF (1227 KB)Optimal Control Problems with a System of Integral Equations and Restricted Phase Coordinates18 July 2006 | SIAM Journal on Control, Vol. 10, No. 1AbstractPDF (1661 KB)The Optimization of Trajectories of Linear Functional Differential Equations18 July 2006 | SIAM Journal on Control, Vol. 8, No. 4AbstractPDF (2777 KB) Volume 6, Issue 2| 1968SIAM Journal on Control History Submitted:06 July 1967Published online:18 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0306016Article page range:pp. 215-234ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics

The Reduction of Certain Control Problems to an “Ordinary Differential” Type

Previous article Next article The Reduction of Certain Control Problems to an “Ordinary Differential” TypeJ. WargaJ. Wargahttps://doi.org/10.1137/1010036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout Previous article Next article FiguresRelatedReferencesCited byDetails Stationarity conditions in optimal control problems class related to dynamical objects group control Cross Ref On the First- and Second-Order Conditions in Optimal Control Problems Related to Autonomous Objects Group lifecycle Cross Ref Optimal Control Problems with Time Delays: Constancy of the HamiltonianRichard B. Vinter25 July 2019 | SIAM Journal on Control and Optimization, Vol. 57, No. 4AbstractPDF (525 KB)On obtaining the stationarity conditions in an optimal control problem for a trajectory with a smooth contact with the phase boundary Cross Ref On one Method to Obtain Stationarity Conditions for an Optimal Control Problem Trajectory With a Smooth Boundary ContactIFAC-PapersOnLine, Vol. 51, No. 32 Cross Ref The Maximum Principle for Optimal Control Problems with Time DelaysA. Boccia and R. B. Vinter19 September 2017 | SIAM Journal on Control and Optimization, Vol. 55, No. 5AbstractPDF (407 KB)Problems with relaxed shifted controls and the pointwise maximum principleNonlinear Analysis: Theory, Methods & Applications, Vol. 75, No. 3 Cross Ref The Instability of Optimal Control Problems to Time DelayAlexey S. Matveev26 July 2006 | SIAM Journal on Control and Optimization, Vol. 43, No. 5AbstractPDF (340 KB)On the Characterization of Properly Relaxed Delayed ControlsJournal of Mathematical Analysis and Applications, Vol. 209, No. 1 Cross Ref Approximation of strongly relaxed minimizers with ordinary delayed controlsApplied Mathematics & Optimization, Vol. 32, No. 1 Cross Ref Jack Warga: In Appreciation14 July 2006 | SIAM Journal on Control and Optimization, Vol. 33, No. 2AbstractPDF (809 KB)Minimizing approximate original solutions for commensurate delayed controlsApplied Mathematics Letters, Vol. 7, No. 5 Cross Ref How to Properly Relax Delayed Controls Cross Ref A proper relaxation of shifted and delayed controlsJournal of Mathematical Analysis and Applications, Vol. 169, No. 2 Cross Ref Optimal controls and their discontinuities in quadratic problems of delay systemsIEEE Transactions on Automatic Control, Vol. 30, No. 7 Cross Ref Optimal Controls with PseudodelaysJ. Warga18 July 2006 | SIAM Journal on Control, Vol. 12, No. 2AbstractPDF (1227 KB)A conservative bound on the estimation error covariance matrix in the presence of correlated driving noise and correlated discrete measurement noiseJournal of Mathematical Analysis and Applications, Vol. 43, No. 2 Cross Ref References Cross Ref Volume 10, Issue 2| 1968SIAM Review History Submitted:18 October 1967Published online:18 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1010036Article page range:pp. 219-222ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

An embedding theorem for differential equations

The present paper establishes a general embedding theorem for differential equations, which is useful in establishing the maximum principle for optimal control problems.

A Maximum Principle for Optimal Control Problems in which the Phase Space Constraint Set is Closed

Previous article Next article A Maximum Principle for Optimal Control Problems in which the Phase Space Constraint Set is ClosedJane CullumJane Cullumhttps://doi.org/10.1137/0304039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Leonard D. Berkovitz, Variational methods in problems of control and programming, J. Math. Anal. Appl., 3 (1961), 145–169 10.1016/0022-247X(61)90013-0 MR0139030 0100.31005 CrossrefGoogle Scholar[2] Leonard D. Berkovitz, On control problems with bounded state variables, J. Math. Anal. Appl., 5 (1962), 488–498 10.1016/0022-247X(62)90020-3 MR0141557 0116.08102 CrossrefGoogle Scholar[3] A. F. Filippov, On certain questions in the theory of optimal control, J. SIAM Control Ser. A, 1 (1962), 76–84, (translation from Russian). 10.1137/0301006 MR0149985 0139.05102 LinkGoogle Scholar[4] T. Guinn, The problem of bounded space coordinates as a problem of Hestenes, J. Soc. Indust. Appl. Math. Ser. A Control, 3 (1965), 181–190 MR0192938 0151.12901 LinkGoogle Scholar[5] E. J. McShane, On multipliers for Lagrange problems, Amer. J. Math., 61 (1939), 809–819 MR0000462 0022.23403 CrossrefGoogle Scholar[6] E. J. McShane, Necessary conditions in generalized-curve problems of the calculus of variations, Duke Math. J., 7 (1940), 1–27 10.1215/S0012-7094-40-00701-3 MR0003478 0024.32503 CrossrefGoogle Scholar[7] I. P. Natanson, Theory of Functions of a Real Variable, Vol. I, Ungar, New York, 1964 Google Scholar[8] 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[9] Walter Rudin, Principles of mathematical analysis, Second edition, McGraw-Hill Book Co., New York, 1964ix+270 MR0166310 0148.02903 Google Scholar[10] J. Warga, Relaxed variational problems, J. Math. Anal. Appl., 4 (1962), 111–128 10.1016/0022-247X(62)90033-1 MR0142020 0102.31801 CrossrefGoogle Scholar[11] J. Warga, Necessary conditions for minimum in relaxed variational problems, J. Math. Anal. Appl., 4 (1962), 129–145 10.1016/0022-247X(62)90034-3 MR0142021 0102.31802 CrossrefGoogle Scholar[12] J. Warga, Minimizing variational curves restricted to a preassigned set, Trans. Amer. Math. Soc., 112 (1964), 432–455 MR0164840 0129.07403 CrossrefGoogle Scholar[13] J. Warga, Unilateral variational problems with several inequalities, Michigan Math. J., 12 (1965), 449–480 10.1307/mmj/1028999428 MR0185482 0137.08401 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 4, Issue 3| 1966SIAM Journal on Control History Submitted:04 February 1966Published online:18 July 2006 InformationCopyright © 1966 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0304039Article page range:pp. 488-504ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics