zbMATH — the first resource for mathematics

A Filippov-type lemma for functions involving delays and its application to time-delayed optimal control problem. (English) Zbl 0377.49006

49J99 Existence theories in calculus of variations and optimal control
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34H05 Control problems involving ordinary differential equations
Full Text: DOI
[1] Ahmed, N. U.,Optimal Control of a Class of Hereditary Systems with Lagging Control, International Journal of Systems Science, Vol. 5, pp. 287-293, 1974. · Zbl 0277.49004 · doi:10.1080/00207727408920095
[2] Angell, T. S.,Existence Theorems for Optimal Control Problems Involving Functional Differential Equations, Journal of Optimization Theory and Applications, Vol. 3, pp. 149-169, 1971. · Zbl 0198.20301 · doi:10.1007/BF00932473
[3] Das, P. C., andSharma, R. R.,On Optimal Controls for Measure Delay Differential Equations, SIAM Journal on Control, Vol. 7, pp. 43-61, 1971. · Zbl 0283.49003 · doi:10.1137/0309005
[4] O?uzt√∂reli, M. N.,Time-Lag Control Systems, Academic Press, New York, New York, 1966. · Zbl 0143.12101
[5] Georganas, N. D., andAhmed, N. U.,Optimal Initial Data and Control for a Class of Linear Hereditary Systems, Information and Control, Vol. 22, pp. 394-402, 1973. · Zbl 0256.49011 · doi:10.1016/S0019-9958(73)90547-0
[6] Nababan, S., andTeo, K. L.,An Existence Theorem for Optimal Controls of Nonlinear Vector Delay Differential Equations with Time-Lag Controls, International Journal of Systems Science, Vol. 8, pp. 1163-1172, 1977. · Zbl 0402.49009 · doi:10.1080/00207727708942111
[7] Fillipov, A. F.,On Certain Questions in the Theory of Optimal Controls, SIAM Journal on Control, Vol. 1, pp. 76-84, 1962.
[8] McShane. E. J., andWarfield, R. B.,On Fillipov’s Implicit Function Lemma, Proceedings of American Mathematical Society, Vol. 18, pp. 41-47, 1967. · Zbl 0145.34403
[9] Jacobs, M. Q.,Attainable Sets in Systems with Unbounded Controls, Journal of Differential Equations, Vol. 4, pp. 408-423, 1968. · Zbl 0172.13501 · doi:10.1016/0022-0396(68)90027-2
[10] Berkovitz, L. D.,Existence Theorems in Problems of Optimal Control, Studia Mathematica, Vol. 65, pp. 275-285, 1972. · Zbl 0215.21406
[11] Cesari, L.,Existence Theorems for Optimal Solutions in Pontryagin and Lagrange Problems, SIAM Journal on Control, Vol. 3, pp. 475-497, 1966. · Zbl 0137.08204
[12] Cesari, L. Closure Theorems for Orientor Fields and Weak Convergence, Archive for Rational Mechanics and Analysis, Vol. 55, pp. 332-356, 1974. · Zbl 0296.49029 · doi:10.1007/BF00250438
[13] Quinn, T.,Reduction of Delayed Optimal Control Problems to Nondelayed Problems, Journal of Optimization Theory and Applications, Vol. 18, pp. 371-379, 1976. · Zbl 0304.49017 · doi:10.1007/BF00933818
[14] Dunford, N., andSchwartz, J. T.,Linear Operators, John Wiley & Sons, Inc., Interscience Publishers, New York, New York, 1958.
[15] McShane, E. J.,Integration, Princeton University Press, Princeton, New Jersey, 1959.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.