Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System

Maysoon M. Aziz; Saad Fawzi AL-Azzawi

doi:doi:10.11648/j.pamj.20170601.12

| Peer-Reviewed

Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System

Maysoon M. Aziz, Saad Fawzi AL-Azzawi

Published in Pure and Applied Mathematics Journal (Volume 6, Issue 1)

Received: 1 January 2017 Accepted: 13 January 2017 Published: 16 February 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This paper investigates the stabilization of unstable equilibrium for a 4D hyperchaotic system. The linear, non-linear and speed feedback controls are used to suppress hyperchaos to this equilibrium. The Routh-Hurwitz theorem and Lyapunov's second methods are used to derive the conditions of the asymptotic stability of the controlled hyperchaotic system. Theoretical analysis, numerical simulation and illustrative examples are given to demonstrate the effectiveness of the proposed controllers.

Published in	Pure and Applied Mathematics Journal (Volume 6, Issue 1)
DOI	10.11648/j.pamj.20170601.12
Page(s)	5-13
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Chaos Control, Linear Feedback Control, Non-linear Feedback Control, Routh-Hurwitz Method, Lyapunov's Second Method

References

[1]	X. Changjin, L. Peiluan, Chaos control for a 4D hyperchaotic system, Applied Mechanics and Materials. 418 (2013) 84-87.
[2]	H. Wang, G. Cai, Controlling hyperchaos in a novel hyperchaotic system, Journal of Information and Computing Science, 4 (2009) 251-258.
[3]	C. Yang, C. H. Tao, P. Wang, Comparison of feedback control methods for a hyperchaotic Lorenz system, Physics Letters A 374 (2010) 729-732.
[4]	C. Zhu, Feedback control method for stabilizing unstable equilibrium points in a new chaotic system, Nonlinear analysis, 71 (2009) 2441-2446.
[5]	C. Zhu, Z. Chen, Feedback control strategies for the Liu chaotic system, Phys. Lett. A 372 (2008) 4033-4036.
[6]	C. Tao, C. Yang, Y. Luo, H. Xiong, F. Hu, Speed feedback control of chaotic system, Chaos Solitons Fractals 23 (2005) 259-263.
[7]	S. Pang, Y. Liu, A new hyperchaotic system from the Lu ̈ system and its control. Journal of Computational and Applied Mathematics, 235 (2011) 2775-2789.
[8]	Z. Yan, Controlling hyperchaos in the new hyperchaotic chen system, Appl. Math. Comput. 168 (2005) 1239-1250.
[9]	Q. Dou, J. A. Sun, W. S. Duan, K. P. Lu ̈, Controlling hyperchaos in the new hyperchaotic system, Commun. Nonlinear Sci. Numer., 14 (2009) 552-559.
[10]	C. Zhu, Controlling hyperchaos in hyperchaotic Lorenz system using feedback controllers, Appl. Math. Comput. 216 (2010) 3126-3132.
[11]	M. M. Aziz, S. F. AL-Azzawi.. Using Feedback Control Methods to Suppress a Modified Hyperchaotic Pan System, Computational and Applied Mathematics Journal. 1 (3), (2015) 97-106.
[12]	M. M. Aziz, S. F. AL-Azzawi, Some Problems of feedback control strategies and its treatment, Journal of Mathematics Research; 9 (1), (2017) 39-49.
[13]	S. F. AL-Azzawi, Study of dynamical properties and effective of a state u for hyperchaotic pan systems, Al-Rafiden J. Comput. Sci. Math. 10 (2013) 89-99.
[14]	S. F. AL-Azzawi, Stability and bifurcation of pan chaotic system by using Routh-Hurwitz and Gardan method, Appl. Math. Comput. 219 (2012) 1144-1152.
[15]	W. Xiang, C. Liang, M. Sheng, T. Xin, Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation, 19 (2010).
[16]	C. Tao, C. Yang, Three control strategies for the Lorenz chaotic system, Chaos Solitons Fractals 35 (2008) 1009-1014.

Cite This Article

Plain Text BibTeX RIS

APA Style

Maysoon M. Aziz, Saad Fawzi AL-Azzawi. (2017). Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System. Pure and Applied Mathematics Journal, 6(1), 5-13. https://doi.org/10.11648/j.pamj.20170601.12

Copy | Download

ACS Style

Maysoon M. Aziz; Saad Fawzi AL-Azzawi. Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System. Pure Appl. Math. J. 2017, 6(1), 5-13. doi: 10.11648/j.pamj.20170601.12

Copy | Download

AMA Style

Maysoon M. Aziz, Saad Fawzi AL-Azzawi. Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System. Pure Appl Math J. 2017;6(1):5-13. doi: 10.11648/j.pamj.20170601.12

Copy | Download

@article{10.11648/j.pamj.20170601.12,
  author = {Maysoon M. Aziz and Saad Fawzi AL-Azzawi},
  title = {Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System},
  journal = {Pure and Applied Mathematics Journal},
  volume = {6},
  number = {1},
  pages = {5-13},
  doi = {10.11648/j.pamj.20170601.12},
  url = {https://doi.org/10.11648/j.pamj.20170601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170601.12},
  abstract = {This paper investigates the stabilization of unstable equilibrium for a 4D hyperchaotic system. The linear, non-linear and speed feedback controls are used to suppress hyperchaos to this equilibrium. The Routh-Hurwitz theorem and Lyapunov's second methods are used to derive the conditions of the asymptotic stability of the controlled hyperchaotic system. Theoretical analysis, numerical simulation and illustrative examples are given to demonstrate the effectiveness of the proposed controllers.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System
AU  - Maysoon M. Aziz
AU  - Saad Fawzi AL-Azzawi
Y1  - 2017/02/16
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170601.12
DO  - 10.11648/j.pamj.20170601.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 5
EP  - 13
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170601.12
AB  - This paper investigates the stabilization of unstable equilibrium for a 4D hyperchaotic system. The linear, non-linear and speed feedback controls are used to suppress hyperchaos to this equilibrium. The Routh-Hurwitz theorem and Lyapunov's second methods are used to derive the conditions of the asymptotic stability of the controlled hyperchaotic system. Theoretical analysis, numerical simulation and illustrative examples are given to demonstrate the effectiveness of the proposed controllers.
VL  - 6
IS  - 1
ER  -

Copy | Download

Author Information

Maysoon M. Aziz

Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq
Saad Fawzi AL-Azzawi

Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Maysoon M. Aziz, Saad Fawzi AL-Azzawi. (2017). Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System. Pure and Applied Mathematics Journal, 6(1), 5-13. https://doi.org/10.11648/j.pamj.20170601.12

Copy | Download

ACS Style

Maysoon M. Aziz; Saad Fawzi AL-Azzawi. Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System. Pure Appl. Math. J. 2017, 6(1), 5-13. doi: 10.11648/j.pamj.20170601.12

Copy | Download

AMA Style

Maysoon M. Aziz, Saad Fawzi AL-Azzawi. Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System. Pure Appl Math J. 2017;6(1):5-13. doi: 10.11648/j.pamj.20170601.12

Copy | Download

@article{10.11648/j.pamj.20170601.12,
  author = {Maysoon M. Aziz and Saad Fawzi AL-Azzawi},
  title = {Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System},
  journal = {Pure and Applied Mathematics Journal},
  volume = {6},
  number = {1},
  pages = {5-13},
  doi = {10.11648/j.pamj.20170601.12},
  url = {https://doi.org/10.11648/j.pamj.20170601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170601.12},
  abstract = {This paper investigates the stabilization of unstable equilibrium for a 4D hyperchaotic system. The linear, non-linear and speed feedback controls are used to suppress hyperchaos to this equilibrium. The Routh-Hurwitz theorem and Lyapunov's second methods are used to derive the conditions of the asymptotic stability of the controlled hyperchaotic system. Theoretical analysis, numerical simulation and illustrative examples are given to demonstrate the effectiveness of the proposed controllers.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System
AU  - Maysoon M. Aziz
AU  - Saad Fawzi AL-Azzawi
Y1  - 2017/02/16
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170601.12
DO  - 10.11648/j.pamj.20170601.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 5
EP  - 13
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170601.12
AB  - This paper investigates the stabilization of unstable equilibrium for a 4D hyperchaotic system. The linear, non-linear and speed feedback controls are used to suppress hyperchaos to this equilibrium. The Routh-Hurwitz theorem and Lyapunov's second methods are used to derive the conditions of the asymptotic stability of the controlled hyperchaotic system. Theoretical analysis, numerical simulation and illustrative examples are given to demonstrate the effectiveness of the proposed controllers.
VL  - 6
IS  - 1
ER  -

Copy | Download