A~numerical method for the minimax solution of the Bellman equation in the Cauchy problem with additional restrictions
Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 208-215
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A new numerical method is suggested for constructing the value function in optimal control problems of prescribed duration with positional running cost along motions of controlled dynamical systems. The algorithm is based on a backward procedure involving characteristics of the Bellman equation. Estimations of the approximation are provided. Results of simulations for a model example are exposed.
@article{TIMM_2006_12_1_a15,
author = {N. N. Subbotina and T. B. Tokmantsev},
title = {A~numerical method for the minimax solution of the {Bellman} equation in the {Cauchy} problem with additional restrictions},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {208--215},
publisher = {mathdoc},
volume = {12},
number = {1},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a15/}
}
TY - JOUR AU - N. N. Subbotina AU - T. B. Tokmantsev TI - A~numerical method for the minimax solution of the Bellman equation in the Cauchy problem with additional restrictions JO - Trudy Instituta matematiki i mehaniki PY - 2006 SP - 208 EP - 215 VL - 12 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a15/ LA - ru ID - TIMM_2006_12_1_a15 ER -
%0 Journal Article %A N. N. Subbotina %A T. B. Tokmantsev %T A~numerical method for the minimax solution of the Bellman equation in the Cauchy problem with additional restrictions %J Trudy Instituta matematiki i mehaniki %D 2006 %P 208-215 %V 12 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a15/ %G ru %F TIMM_2006_12_1_a15
N. N. Subbotina; T. B. Tokmantsev. A~numerical method for the minimax solution of the Bellman equation in the Cauchy problem with additional restrictions. Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 208-215. http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a15/