Geodesic
Construction of the reachable set for a two-dimensional bilinear impulsive control system
The Bulletin of Irkutsk State University. Series Mathematics, Tome 15 (2016), pp. 3-16

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper deals with a problem of construction of the reachable set for an impulsive control system with trajectories of bounded variation and impulsive controls (regular vector measures). The considered control system has a bilinear structure relative to the control variable. A method for constructing of the boundary of the reachable set is proposed. This method is based on using of special impulsive optimal control problems and Lyapunov type functions. These functions are strongly monotone relative to the impulsive control system. Presented results are illustrated by a numerical example. An algorithm of numerical approximation of reachable sets for nonlinear impulsive control systems is discussed. This algorithm is realized in the Scientific Python environment.
Keywords: measure-driven impulsive control system, trajectories of bounded variation, reachable set, monotone of Lyapunov type functions, numerical methods. 
@article{IIGUM_2016_15_a0,
     author = {D. V. Apanovich and V. A. Voronov and O. N. Samsonyuk},
     title = {Construction of the reachable set for a two-dimensional bilinear impulsive control system},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {3--16},
     publisher = {mathdoc},
     volume = {15},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2016_15_a0/}
}
TY  - JOUR
AU  - D. V. Apanovich
AU  - V. A. Voronov
AU  - O. N. Samsonyuk
TI  - Construction of the reachable set for a two-dimensional bilinear impulsive control system
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2016
SP  - 3
EP  - 16
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2016_15_a0/
LA  - ru
ID  - IIGUM_2016_15_a0
ER  - 
%0 Journal Article
%A D. V. Apanovich
%A V. A. Voronov
%A O. N. Samsonyuk
%T Construction of the reachable set for a two-dimensional bilinear impulsive control system
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2016
%P 3-16
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIGUM_2016_15_a0/
%G ru
%F IIGUM_2016_15_a0
D. V. Apanovich; V. A. Voronov; O. N. Samsonyuk. Construction of the reachable set for a two-dimensional bilinear impulsive control system. The Bulletin of Irkutsk State University. Series Mathematics, Tome 15 (2016), pp. 3-16. http://geodesic.mathdoc.fr/item/IIGUM_2016_15_a0/