Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation

Anar Huseyin; Nesir Huseyin

Applications of Mathematics (2014)

  • Volume: 59, Issue: 3, page 303-317
  • ISSN: 0862-7940

Abstract

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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 μ 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 μ for each fixed p , and is continuous with respect to p for each fixed μ . An upper estimate for the diameter of the set of trajectories is given.

How to cite

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Huseyin, Anar, and 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 59.3 (2014): 303-317. <http://eudml.org/doc/261186>.

@article{Huseyin2014,
abstract = {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.},
author = {Huseyin, Anar, Huseyin, Nesir},
journal = {Applications of Mathematics},
keywords = {nonlinear Volterra integral equation; control system; integral constraint; nonlinear Volterra integral equation; control system; integral constraint; Lipschitz continuous solutions},
language = {eng},
number = {3},
pages = {303-317},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation},
url = {http://eudml.org/doc/261186},
volume = {59},
year = {2014},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 303
EP - 317
AB - 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.
LA - eng
KW - nonlinear Volterra integral equation; control system; integral constraint; nonlinear Volterra integral equation; control system; integral constraint; Lipschitz continuous solutions
UR - http://eudml.org/doc/261186
ER -

References

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