Geodesic
Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation
Applications of Mathematics, Tome 59 (2014) no. 3, pp. 303-317.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius $\mu $ in $L_p$ $(p>1)$. It is proved that the set of trajectories generated by all admissible control functions is Lipschitz continuous with respect to $\mu $ for each fixed $p$, and is continuous with respect to $p$ for each fixed $\mu $. An upper estimate for the diameter of the set of trajectories is given.
DOI : 10.1007/s10492-014-0056-4
Classification : 45D05, 93B03, 93C23
Keywords: nonlinear Volterra integral equation; control system; integral constraint 
@article{10_1007_s10492_014_0056_4,
     author = {Huseyin, Anar and Huseyin, Nesir},
     title = {Dependence on the parameters of the set of trajectories of the control system described by a nonlinear {Volterra} integral equation},
     journal = {Applications of Mathematics},
     pages = {303--317},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {2014},
     doi = {10.1007/s10492-014-0056-4},
     mrnumber = {3232632},
     zbl = {06362228},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0056-4/}
}
TY  - JOUR
AU  - Huseyin, Anar
AU  - Huseyin, Nesir
TI  - Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation
JO  - Applications of Mathematics
PY  - 2014
SP  - 303
EP  - 317
VL  - 59
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0056-4/
DO  - 10.1007/s10492-014-0056-4
LA  - en
ID  - 10_1007_s10492_014_0056_4
ER  - 
%0 Journal Article
%A Huseyin, Anar
%A Huseyin, Nesir
%T Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation
%J Applications of Mathematics
%D 2014
%P 303-317
%V 59
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0056-4/
%R 10.1007/s10492-014-0056-4
%G en
%F 10_1007_s10492_014_0056_4
Huseyin, Anar; Huseyin, Nesir. Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation. Applications of Mathematics, Tome 59 (2014) no. 3, pp. 303-317. doi : 10.1007/s10492-014-0056-4. http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0056-4/

Cité par Sources :