Null controllability of a nonlinear diffusion system in reactor dynamics

Kumarasamy Sakthivel; Krishnan Balachandran; Jong-Yeoul Park; Ganeshan Devipriya

Kybernetika (2010)

  • Volume: 46, Issue: 5, page 890-906
  • ISSN: 0023-5954

Abstract

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In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of ℝ with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients. Then this result is successfully used with some estimates for parabolic equation in L k spaces together with classical fixed point theorem, to prove the null controllability of the nonlinear model.

How to cite

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Sakthivel, Kumarasamy, et al. "Null controllability of a nonlinear diffusion system in reactor dynamics." Kybernetika 46.5 (2010): 890-906. <http://eudml.org/doc/196372>.

@article{Sakthivel2010,
abstract = {In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of $\mathbb \{R\}$ with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients. Then this result is successfully used with some estimates for parabolic equation in $L^k$ spaces together with classical fixed point theorem, to prove the null controllability of the nonlinear model.},
author = {Sakthivel, Kumarasamy, Balachandran, Krishnan, Park, Jong-Yeoul, Devipriya, Ganeshan},
journal = {Kybernetika},
keywords = {controllability; observability; parabolic integrodifferential equation; controllability; observability; parabolic integrodifferential equation},
language = {eng},
number = {5},
pages = {890-906},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Null controllability of a nonlinear diffusion system in reactor dynamics},
url = {http://eudml.org/doc/196372},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Sakthivel, Kumarasamy
AU - Balachandran, Krishnan
AU - Park, Jong-Yeoul
AU - Devipriya, Ganeshan
TI - Null controllability of a nonlinear diffusion system in reactor dynamics
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 5
SP - 890
EP - 906
AB - In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of $\mathbb {R}$ with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients. Then this result is successfully used with some estimates for parabolic equation in $L^k$ spaces together with classical fixed point theorem, to prove the null controllability of the nonlinear model.
LA - eng
KW - controllability; observability; parabolic integrodifferential equation; controllability; observability; parabolic integrodifferential equation
UR - http://eudml.org/doc/196372
ER -

References

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