On the Robustness Property of a Control System Described by an Urysohn Type Integral Equation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 3, pp. 263-270
Voir la notice de l'article provenant de la source Math-Net.Ru
In this paper a control system described by an Urysohn type integral equation with an integral constraint on the control functions is studied. It is assumed that the system is nonlinear with respect to the state vector and is affine with respect to the control vector. The control functions are chosen from a closed ball of the space $L_p$ $(p>1)$ with radius $r$. It is proved that the set of trajectories of the control system generated by all admissible control functions is Lipschitz continuous with respect to $r$ and is continuous with respect to $p$ as a set valued map. It is shown that the system's trajectory is robust with respect to the full consumption of the remaining control resource and every trajectory can be approximated by a trajectory generated by the control function with full control resource consumption.
Keywords:
integral equation, control system, integral constraint, set of trajectories, robustness.
@article{TIMM_2021_27_3_a21,
author = {N. Huseyin and A. Huseyin and Kh. G. Guseinov},
title = {On the {Robustness} {Property} of a {Control} {System} {Described} by an {Urysohn} {Type} {Integral} {Equation}},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {263--270},
publisher = {mathdoc},
volume = {27},
number = {3},
year = {2021},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a21/}
}
TY - JOUR AU - N. Huseyin AU - A. Huseyin AU - Kh. G. Guseinov TI - On the Robustness Property of a Control System Described by an Urysohn Type Integral Equation JO - Trudy Instituta matematiki i mehaniki PY - 2021 SP - 263 EP - 270 VL - 27 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a21/ LA - en ID - TIMM_2021_27_3_a21 ER -
%0 Journal Article %A N. Huseyin %A A. Huseyin %A Kh. G. Guseinov %T On the Robustness Property of a Control System Described by an Urysohn Type Integral Equation %J Trudy Instituta matematiki i mehaniki %D 2021 %P 263-270 %V 27 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a21/ %G en %F TIMM_2021_27_3_a21
N. Huseyin; A. Huseyin; Kh. G. Guseinov. On the Robustness Property of a Control System Described by an Urysohn Type Integral Equation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 3, pp. 263-270. http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a21/