Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria

Hassan Saberi Nik; Ping He; Sayyed Taha Talebian

Kybernetika (2014)

  • Volume: 50, Issue: 4, page 596-615
  • ISSN: 0023-5954

Abstract

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In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose Lyapunov stability to control the Pehlivan-Uyaroglu system with unknown parameters by way of a feedback control approach and a single controller. Numerical simulations are performed to demonstrate the effectiveness of the proposed control strategies.

How to cite

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Saberi Nik, Hassan, He, Ping, and Talebian, Sayyed Taha. "Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria." Kybernetika 50.4 (2014): 596-615. <http://eudml.org/doc/261993>.

@article{SaberiNik2014,
abstract = {In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose Lyapunov stability to control the Pehlivan-Uyaroglu system with unknown parameters by way of a feedback control approach and a single controller. Numerical simulations are performed to demonstrate the effectiveness of the proposed control strategies.},
author = {Saberi Nik, Hassan, He, Ping, Talebian, Sayyed Taha},
journal = {Kybernetika},
keywords = {autonomous chaotic system; optimal control; adaptive control; single state feedback control; Pontryagin Minimum Principle; autonomous chaotic system; optimal control; adaptive control; single state feedback control; Pontryagin minimum principle},
language = {eng},
number = {4},
pages = {596-615},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria},
url = {http://eudml.org/doc/261993},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Saberi Nik, Hassan
AU - He, Ping
AU - Talebian, Sayyed Taha
TI - Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 4
SP - 596
EP - 615
AB - In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose Lyapunov stability to control the Pehlivan-Uyaroglu system with unknown parameters by way of a feedback control approach and a single controller. Numerical simulations are performed to demonstrate the effectiveness of the proposed control strategies.
LA - eng
KW - autonomous chaotic system; optimal control; adaptive control; single state feedback control; Pontryagin Minimum Principle; autonomous chaotic system; optimal control; adaptive control; single state feedback control; Pontryagin minimum principle
UR - http://eudml.org/doc/261993
ER -

References

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