On the set-valued calculus in problems of viability and control for dynamic processes : the evolution equation
A. B. Kurzhanski; T. F. Filippova
Annales de l'I.H.P. Analyse non linéaire (1989)
- Volume: S6, page 339-363
- ISSN: 0294-1449
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topKurzhanski, A. B., and Filippova, T. F.. "On the set-valued calculus in problems of viability and control for dynamic processes : the evolution equation." Annales de l'I.H.P. Analyse non linéaire S6 (1989): 339-363. <http://eudml.org/doc/78202>.
@article{Kurzhanski1989,
author = {Kurzhanski, A. B., Filippova, T. F.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {viability; funnel equation; evolution equation; differential inclusion; directional derivative},
language = {eng},
pages = {339-363},
publisher = {Gauthier-Villars},
title = {On the set-valued calculus in problems of viability and control for dynamic processes : the evolution equation},
url = {http://eudml.org/doc/78202},
volume = {S6},
year = {1989},
}
TY - JOUR
AU - Kurzhanski, A. B.
AU - Filippova, T. F.
TI - On the set-valued calculus in problems of viability and control for dynamic processes : the evolution equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - S6
SP - 339
EP - 363
LA - eng
KW - viability; funnel equation; evolution equation; differential inclusion; directional derivative
UR - http://eudml.org/doc/78202
ER -
References
top- 1. Krasovski, N.N., The Control of a Dynamic System, Moscow, "Nauka", 1986 (in Russian). MR820965
- 2. Kurzhanski, A.B., On the analytical description of the set of viable trajectories of a differential system, Dokl. Acad. Nauk SSSR, 1986, 287, 5, pp. 1047-1050 (in Russian). Zbl0613.34010MR839699
- 3. Kurzhanski, A.B., Filippova, T.F.On the description of the set of viable trajectories of a differential inclusion, Dokl. Acad. Nauk SSSR, 1986, 289, 1, pp. 38-41 (in Russian). Zbl0622.34011MR852286
- 4. Kurzhanski, A.B., Filippova, T.F.On the description of the set of viable trajectories of a control system, Different. Uravn., 1987, No. 8, pp. 1303-1315 (in Russian). Zbl0637.49018MR909576
- 5. Aubin, J.-P., Cellina A., Differential inclusions, Heidelberg, Springer-Verlag, 1984. Zbl0538.34007MR755330
- 6. Kurzhanski, A.B., Control and observation under uncertainty, Moscow, "Nauka", 1977 (in Russian).
- 7. Castaing, C., Valadier, M., Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol. 580, Springer-Verlag, 1977. Zbl0346.46038MR467310
- 8. Aubin, J.-P., Ekeland I., Applied nonlinear analysis, New York, Academic Press, 1984. Zbl0641.47066MR749753
- 9. Panasyuk, A.I., Panasyuk V.I., Asymptotic magistral optimization of control systems, Minsk, "Nauka i Tekhika", 1986 (in Russian). Zbl0613.49003MR854866
- 10. Tolstonogov, A.A., Differential inclusions in Banach space, Novosibirsk, "Nauka", 1986 (in Russian). Zbl0689.34014
- 11. Blagodatskikh, V.I., Filippov A.F., Differential inclusions and optimal control, Trudy Matem. Inst. Akad. Nauk SSSR, 169, Moscow, "Nauka", 1985 (in Russian). Zbl0595.49026MR836575
- 12. Demyanov, V.F., Lemaréchal C., Zowe J., Approximation to a set-valued mapping, I: a proposal, Appl. Math. Optim., 1986, 14, 3, p. 203-214. Zbl0619.49005MR867718
- 13. Joffe, A.D., Tihomirov, V.M., The theory of extremal problems, Moscow, "Nauka", 1979. Zbl0407.90051
- 14. Kurzhanski, A.B. and Osipov, Yu.S.On optimal control under state constraints. Prikladnaia Matematika i Mehanika (Applied Mathematics and Mechanics) vol. 33, No. 4, 1969.
- 15. Rockafellar, R.T., State Constraints in Convex Problems of Bolza. SIAM J. Control. vol. 10, No. 4, 1972. Zbl0224.49003MR324505
- 16. Demianov, V.F., Minimax: directional differentiation. LeningradUniversity Press, 1974. MR445825
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