Title:
|
Necessary optimality conditions for discrete systems with state-dependent control region (English) |
Author:
|
Doležal, Jaroslav |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
11 |
Issue:
|
6 |
Year:
|
1975 |
Pages:
|
(423)-450 |
. |
Category:
|
math |
. |
MSC:
|
49K99 |
MSC:
|
49M99 |
MSC:
|
90C30 |
MSC:
|
90C50 |
MSC:
|
90C90 |
MSC:
|
93C55 |
idZBL:
|
Zbl 0321.49014 |
idMR:
|
MR0401278 |
. |
Date available:
|
2009-09-24T16:48:31Z |
Last updated:
|
2012-06-05 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125733 |
. |
Reference:
|
[1] M. Canon C. Cullum E. Polak: Constrained minimization problems in finite dimensional spaces.SIAM J. Control 4 (1966), 3, 528-547. MR 0207423 |
Reference:
|
[2] N. O. DaCunha E. Polak: Constrained minimization under vector-valued criteria in finite dimensional spaces.J. Math. Anal. Applies. 19 (1967), 1, 103-124. MR 0216346 |
Reference:
|
[3] M. D. Canon C. D. Cullum E. Polak: Theory of Optimal Control and Mathematical Programming.McGraw-Hill, New York 1970. MR 0397497 |
Reference:
|
[4] A. Blaqiuère F. Gérard G. Leitman: Quantitative and Qualitative Games.Academic Press, New York 1969. MR 0261973 |
Reference:
|
[5] B. Г. Болтянский: Оптимальное управление дискретным системами.Наука, Москва 1973. Zbl 1170.01397 |
Reference:
|
[6] L. S. Pontrjagin V. G. Boltjanskij R. V. Gamkrelidze J. F. Miščenko: Matematická teorie optimálních procesů.SNTL, Praha 1964. |
Reference:
|
[7] M. R. Hestenes: Calculus of Variations and Optimal Control Theory.Wiley and Sons, New York 1966. Zbl 0173.35703, MR 0203540 |
Reference:
|
[8] A. Я. Дубовицкий А. А. Милютин: Задачи на экстремум при надичии ограничений.Журнал выч. математики и мат. физики 5 (1965), 3, 395-453. Zbl 1225.00032, MR 0191691 |
Reference:
|
[9] L. W. Neustadt: A general theory of extremals.J. Comp. Syst. Sci. 3 (1969), 1, 57-92. Zbl 0167.08802, MR 0243405 |
Reference:
|
[10] P. B. Гамкрелидзе Г. Л. Харатишвили: Экстремальные задачи в линейных топологических пространствах.Изв. AH CCCP сер. мат. 33 (1969) 4, 781-839. Zbl 1231.90028 |
Reference:
|
[11] R. V. Gamkrelidze: First-order necessary conditions and axiomatics for extremal problems.Proc. Steklov Inst. Math. 112 (1971), 156-186. MR 0331169 |
Reference:
|
[12] J. Doležal: Problémy diskrétního optimálního řízení a diferenční hry.Thesis ÚTIA ČSAV, Praha 1973. |
Reference:
|
[13] J. Doležal: Existence of optimal solutions in general discrete systems.Kybernetika 11 (1975), 4, 301-312. MR 0490220 |
Reference:
|
[14] J. M. Holtzman: Convexity and maximum principle for discrete systems.IEEE Trans. Autom. Contr. AC-11 (1966), 1, 30-35. MR 0191693 |
Reference:
|
[15] J. M. Holtzman: On the maximum principle for non-linear discrete-time systems.IEEE Trans. Autom. Contr. AC-11 (1966), 4, 273-274. MR 0191693 |
Reference:
|
[16] J. M. Holtzman H. Halkin: Directional convexity and the maximum principle for discrete systems.SIAM J. Control 4 (1966), 2, 263-275. MR 0199008 |
Reference:
|
[17] H. Halkin: A maximum principle of the Pontryagin type for systems described by nonlinear difference equations.SIAM J. Control 4 (1966), 1, 90-111. Zbl 0152.09301, MR 0199005 |
Reference:
|
[18] A. И. Пропой: Элементы теории оптимальных дискретных процессов.Наука, Москва 1973. Zbl 1170.01397 |
Reference:
|
[19] C. Olech: Existence theorems for optimal problems with vector-valued cost function.Trans. Amer. Math. Soc. 136 (1969), 159-180. Zbl 0179.14002, MR 0234338 |
Reference:
|
[20] B. Г. Болтянсий: Математические методы оптимального управления.Наука, Москва 1969. Zbl 1149.62317 |
Reference:
|
[21] B. И. Благодатских: Достаточие условия оптимальности.Дифференциальные уравнения 9 (1973), 416-422. Zbl 1170.01397, MR 0322626 |
Reference:
|
[22] W. F. Hogan: Point to set maps in mathematical programming.SIAM Review 15 (1973), 3, 591-603. Zbl 0256.90042, MR 0345641 |
Reference:
|
[23] J. Doležal: Some properties of nonzero-sum multistage games.Preprints of the 6th IFIP Technical Conference on Optimization Techniques. Novosibirsk 1974. |
Reference:
|
[24] J. Doležal: Open-loop hierarchical solution of multistage games.Proceedings of the 2nd Formator Symposium, Prague 1974. Academia, Praha 1975. |
Reference:
|
[25] R. E. Bellman: Dynamic Programming.Princeton Univ. Press, Princeton, New Jersey 1957. Zbl 0995.90618 |
Reference:
|
[26] G. Leitmann: An Introduction to Optimal Control.McGraw-Hill, New York 1966. Zbl 0196.46302 |
Reference:
|
[27] S. A. W. Drew: The application of hierarchical control methods to a managerial problem.Int. J. Systems Sci. 6 (1975), 4, 371-395. Zbl 0367.90057, MR 0424216 |
Reference:
|
[28] P. S. Ritch: Discrete optimal control with multiple constraints I.: Constraint separation and transformation technique.Automatica 9 (1973), 4, 415-429. Zbl 0256.49034, MR 0439328 |
Reference:
|
[29] P. S. Ritch: Discrete optimal control with multiple constraints II: The batch crystallisation of sugar.Automatica 9 (1973), 4, 431-440. MR 0439329 |
. |