Research Article | OPEN ACCESS
Stabilizations of Strange Attractors by Feedback Linearization
1T. Shaqarin, 1N. Alshabatat and 2B.R. Noack
1Department of Mechanical Engineering, College of Engineering, Tafila Technical University, Tafila 66110, Jordan
2D
Research Journal of Applied Sciences, Engineering and Technology 2014 1:43-47
Received: January 31, 2014 | Accepted: February 15, 2014 | Published: July 05, 2014
Abstract
This study deals with the control of the Lorenz, Chen and Lu chaotic system. Feedback linearization was successfully implemented on these chaotic systems. Feedback linearization was successful to transform the three attractor systems to a general system that simplify the linear control analysis. Hence, a linear controller is designed for the feedback linearized general system. Furthermore, some numerical simulations were carried out for the closed loop systems. These simulations show that the developed controller design method is effective in stabilizing and regulating the response.
Keywords:
Chen attractor, feedback linearization, Lorenz attractor , Lu attractor , nonlinear control,
References
-
Alvarez-Gallegos, J., 1994. Nonlinear regulation of a Lorenz system by feedback linearization techniques. Dynam. Control, 4: 277-298.
CrossRef -
Chen, G. and T. Ueta, 1999. Yet another chaotic attractor. Int. J. Bifurcat. Chaos, 9: 1465-1466.
CrossRef -
Chiang, T.Y., M.L. Hung, J.J. Yan, Y.S. Yang and J.F. Chang, 2007. Sliding mode control for uncertain unified chaotic systems with input nonlinearity. Chaos Soliton. Fract., 34(2): 437-424.
CrossRef -
Ge, S.S., C. Wang and T.H. Lee, 2000. Adaptive backstepping control of a class of chaotic systems. Proceedings of the 38th IEEE Conference on Decision and Control, pp: 714-719.
CrossRef -
Li, G.H., 2006. Projective synchronization of chaotic system using backstepping control. Chaos Soliton. Fract., 29: 490-494.
CrossRef -
Lorenz, E.N., 1963. Deterministic nonperiodic flow. J. Atmos. Sci., 20: 130-141.
CrossRef -
Lu, J. and G. Chen, 2002. A new chaotic attractor coined. Int. J. Bifurcat. Chaos, 12: 659-661.
CrossRef -
Nazzal, J.M. and A.N. Natsheh, 2007. Chaos control using sliding-mode theory. Chaos Soliton. Fract., 33: 695-702.
CrossRef -
Pishkenari, H.N., M. Shahrokhi and S.H. Mahboobi, 2007. Adaptive regulation and set-point tracking of the Lorenz attractor. Chaos Soliton. Fract., 32: 832-846.
CrossRef
Competing interests
The authors have no competing interests.
Open Access Policy
This article is 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, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
|
|
|
ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
|
Information |
|
|
|
Sales & Services |
|
|
|