Some Sufficient Conditions for Optimality in Control Problems with State Space Constraints

Previous article Next article Some Sufficient Conditions for Optimality in Control Problems with State Space ConstraintsJ. E. Funk and E. G. GilbertJ. E. Funk and E. G. Gilberthttps://doi.org/10.1137/0308036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] T. Guinn, Weakened hypotheses for the variational problem considered by Hestenes, J. Soc. Indust. Appl. Math. Ser. A Control, 3 (1965), 418–423 MR0192939 0136.09702 LinkGoogle Scholar[2] 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[3] E. B. Lee, A sufficient condition in the theory of optimal control, J. Soc. Indust. Appl. Math. Ser. A Control, 1 (1963), 241–245 MR0175693 0151.13105 LinkGoogle Scholar[4] E. B. Lee and , L. Markus, Foundations of optimal control theory, John Wiley & Sons Inc., New York, 1967x+576 MR0220537 0159.13201 Google Scholar[5] O. L. Mangasarian, Sufficient conditions for the optimal control of nonlinear systems, SIAM J. Control, 4 (1966), 139–152 10.1137/0304013 MR0189864 0154.10401 LinkGoogle Scholar[6] L. L. Schumaker, Approximation by splines, Theory and Applications of Spline Functions (Proceedings of Seminar, Math. Research Center, Univ. of Wisconsin, Madison, Wis., 1968), Academic Press, New York, 1969, 65–85 MR0239329 0187.32802 Google Scholar[7] Lucien W. Neustadt, An abstract variational theory with applications to a broad class of optimization problems. II. Applications, SIAM J. Control, 5 (1967), 90–137 10.1137/0305007 MR0237210 0172.12903 LinkGoogle Scholar[8] Lucien W. Neustadt, A general theory of extremals, J. Comput. System Sci., 3 (1969), 57–92 MR0243405 0167.08802 CrossrefGoogle Scholar[9] 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[10] J. Warga, Minimizing variational curves restricted to a preassigned set, Trans. Amer. Math. Soc., 112 (1964), 432–455 MR0164840 0129.07403 CrossrefGoogle Scholar[11] 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 A Survey of the Maximum Principles for Optimal Control Problems with State ConstraintsRichard F. Hartl, Suresh P. Sethi, and Raymond G. Vickson17 February 2012 | SIAM Review, Vol. 37, No. 2AbstractPDF (4218 KB)A Direct Sufficient Condition for Free Final Time Optimal Control ProblemsP. M. Mereau and W. F. Powers18 July 2006 | SIAM Journal on Control and Optimization, Vol. 14, No. 4AbstractPDF (765 KB)An Example of a Continuous Junction for a Singular Control Problem of Even OrderHelmut Maurer18 July 2006 | SIAM Journal on Control, Vol. 13, No. 4AbstractPDF (324 KB)The Linear Quadratic Cost Problem with Linear State Constraints and the Nonsymmetric Riccati EquationD. D. Thompson and R. A. Volz18 July 2006 | SIAM Journal on Control, Vol. 13, No. 1AbstractPDF (2795 KB)Control of Functional Differential Equations of Retarded and Neutral Type to Target Sets in Function SpaceH. T. Banks and G. A. Kent18 July 2006 | SIAM Journal on Control, Vol. 10, No. 4AbstractPDF (2496 KB)State Constraints in Convex Control Problems of BolzaR. Tyrrell Rockafellar18 July 2006 | SIAM Journal on Control, Vol. 10, No. 4AbstractPDF (2352 KB) Volume 8, Issue 4| 1970SIAM Journal on Control History Submitted:04 September 1969Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0308036Article page range:pp. 498-504ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics