Geodesic
On elimination of state constraints in the construction of reachable sets
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 106-115

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

The paper is devoted to the problem of approximating reachable sets of a nonlinear control system with state constraints given as a solution set of a nonlinear inequality. A state constraint elimination procedure based on the introduction of an auxiliary constraint-free control system is proposed. The equations of the auxiliary system depend on a small parameter. It is shown that the reachable set of the original system can be approximated in the Hausdorff metric by reachable sets of the auxiliary control system as the small parameter tends to zero. Estimates of the convergence rate are given.
Keywords: reachable set, state constraints, penalty function, approximation, Hausdorff metric. 
@article{TIMM_2014_20_4_a9,
     author = {M. I. Gusev},
     title = {On elimination of state constraints in the construction of reachable sets},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {106--115},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a9/}
}
TY  - JOUR
AU  - M. I. Gusev
TI  - On elimination of state constraints in the construction of reachable sets
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2014
SP  - 106
EP  - 115
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a9/
LA  - ru
ID  - TIMM_2014_20_4_a9
ER  - 
%0 Journal Article
%A M. I. Gusev
%T On elimination of state constraints in the construction of reachable sets
%J Trudy Instituta matematiki i mehaniki
%D 2014
%P 106-115
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a9/
%G ru
%F TIMM_2014_20_4_a9
M. I. Gusev. On elimination of state constraints in the construction of reachable sets. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 106-115. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a9/