The continuous dependence of the solution of the controllability problem on the initial and the terminal states for the triangular nonlinearizable systems
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 2, pp. 189-204
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V. I. Korobov; S. S. Pavlichkov. The continuous dependence of the solution of the controllability problem on the initial and the terminal states for the triangular nonlinearizable systems. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 2, pp. 189-204. http://geodesic.mathdoc.fr/item/JMAG_2001_8_2_a6/
@article{JMAG_2001_8_2_a6,
author = {V. I. Korobov and S. S. Pavlichkov},
title = {The continuous dependence of the solution of the controllability problem on the initial and the terminal states for the triangular nonlinearizable systems},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {189--204},
year = {2001},
volume = {8},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/JMAG_2001_8_2_a6/}
}
TY - JOUR
AU - V. I. Korobov
AU - S. S. Pavlichkov
TI - The continuous dependence of the solution of the controllability problem on the initial and the terminal states for the triangular nonlinearizable systems
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 2001
SP - 189
EP - 204
VL - 8
IS - 2
UR - http://geodesic.mathdoc.fr/item/JMAG_2001_8_2_a6/
LA - ru
ID - JMAG_2001_8_2_a6
ER -
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%A V. I. Korobov
%A S. S. Pavlichkov
%T The continuous dependence of the solution of the controllability problem on the initial and the terminal states for the triangular nonlinearizable systems
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2001
%P 189-204
%V 8
%N 2
%U http://geodesic.mathdoc.fr/item/JMAG_2001_8_2_a6/
%G ru
%F JMAG_2001_8_2_a6
Sufficient conditions for the existence of a family of controls $u_{(x^0, x^T)}(\cdot)$, steering the state $x^0 \in{\mathbf R}^n$ into the state $x^T\in{\mathbf R}^n$, for all $x^0\in{\mathbf R}^n$ and $x^T\in{\mathbf R}^n$, and continuously depending on $x^0\in{\mathbf R}^n$ and $x^T\in{\mathbf R}^n$, are given for a class of triangular systems whose trajectories, in general, can not be mapped by a diffeomorphism onto the trajectories of a linear canonical system. As a corollary, the complete controllability of the uniformly bounded perturbations of this class is obtained under the global Lipschitz condition for the right-hand side with respect to $x$ and $u$.
