1Department of Applied Mathematics and Statistics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska dolina, 84248 Bratislava 2Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovicova 3, 81219 Bratislava
Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 79-96
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Pavol Brunovský; Michal Zákopčan; Pavol Brunovský; Michal Zákopčan. Equilibria and stable paths in infinite horizon nonlinear control problems: the linear-quadratic approximation. Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 79-96. http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a7/
@article{AMUC_2015_84_1_a7,
author = {Pavol Brunovsk\'y and Michal Z\'akop\v{c}an and Pavol Brunovsk\'y and Michal Z\'akop\v{c}an},
title = { Equilibria and stable paths in infinite horizon nonlinear control problems: the linear-quadratic approximation},
journal = {Acta mathematica Universitatis Comenianae},
pages = {79--96},
year = {2015},
volume = {84},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a7/}
}
TY - JOUR
AU - Pavol Brunovský
AU - Michal Zákopčan
AU - Pavol Brunovský
AU - Michal Zákopčan
TI - Equilibria and stable paths in infinite horizon nonlinear control problems: the linear-quadratic approximation
JO - Acta mathematica Universitatis Comenianae
PY - 2015
SP - 79
EP - 96
VL - 84
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a7/
ID - AMUC_2015_84_1_a7
ER -
%0 Journal Article
%A Pavol Brunovský
%A Michal Zákopčan
%A Pavol Brunovský
%A Michal Zákopčan
%T Equilibria and stable paths in infinite horizon nonlinear control problems: the linear-quadratic approximation
%J Acta mathematica Universitatis Comenianae
%D 2015
%P 79-96
%V 84
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a7/
%F AMUC_2015_84_1_a7
Nonlinear discrete time innite horizon problems with discount arediscussed. It is shown that if the limit problem without discount admits a nondegenerate steady state "extremal" solution and certain additional hypotheses are satised then for suciently small discounts the steady state solution exists, for initial conditions suciently close to it the problem has a solution of the stable path type and that it can be approximated by the linear-quadratic truncation of the problem.
