Fractional-Order Control for a Novel Chaotic System Without Equilibrium

Shuyi Shao; Mou Chen

doi:10.1109/JAS.2016.7510124

Volume 6 Issue 4

Jul. 2019

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2019 > 6(4): 1000-1009

Shuyi Shao and Mou Chen, "Fractional-Order Control for a Novel Chaotic System Without Equilibrium," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1000-1009, June 2019. doi: 10.1109/JAS.2016.7510124

Citation:

Shuyi Shao and Mou Chen, "Fractional-Order Control for a Novel Chaotic System Without Equilibrium," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1000-1009, June 2019. doi: 10.1109/JAS.2016.7510124

Shuyi Shao and Mou Chen, "Fractional-Order Control for a Novel Chaotic System Without Equilibrium," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1000-1009, June 2019. doi: 10.1109/JAS.2016.7510124

Citation:

Shuyi Shao and Mou Chen, "Fractional-Order Control for a Novel Chaotic System Without Equilibrium," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1000-1009, June 2019. doi: 10.1109/JAS.2016.7510124

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Fractional-Order Control for a Novel Chaotic System Without Equilibrium

doi: 10.1109/JAS.2016.7510124

College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Funds:

the National Natural Science Foundation of China 61573184

Jiangsu Natural Science Foundation of China SBK20130033

Six Talents Peak Project of Jiangsu Province 2012-XXRJ-010

Fundamental Research Funds for the Central Universities NE2016101

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Author Bio:

Shuyi Shao received the M.S. degree in control theory and control engineering from Nanjing Normal University, Nanjing, China, in 2014, and the Ph.D. degree in control theory and control engineering from the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2019. From March 2017 to September 2017 and March 2018 to March 2019, he was a Visiting Scholar with the Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Quebec, Canada. His research interests include fractional-order nonlinear system control, applications of chaos synchronization, and flight control. (e-mail: shaosy@163.com)

Mou Chen (M'10) received the B.S. degree in material science and engineering in 1998 and the M.S. and Ph.D. degrees in automatic control engineering from the Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 1998 and 2004, respectively. He is currently a Full Professor at the College of Automation Engineering at NUAA. He was an academic visitor in the Department of Aeronautical and Automotive Engineering at Loughborough University, U.K., from November 2007 to February 2008. From June 2008 to September 2009, he was a Research Fellow in the Department of Electrical and Computer Engineering at the National University of Singapore. He was a senior academic visitor at the School of Electrical and Electronic Engineering at the University of Adelaide, Australia, from May 2014 to November 2014. His research interests include nonlinear system control, intelligent control, and flight control. (e-mail: chenmou@nuaa.edu.cn)
Corresponding author:
Mou Chen, e-mail: chenmou@nuaa.edu.cn
Received Date: 2015-08-17
Revised Date: 2015-10-30
Accepted Date: 2016-04-18

Abstract

Abstract

The control problem is discussed for a chaotic system without equilibrium in this paper. On the basis of the linear mathematical model of the two-wheeled self-balancing robot, a novel chaotic system which has no equilibrium is proposed. The basic dynamical properties of this new system are studied via Lyapunov exponents and Poincaré map. To further demonstrate the physical realizability of the presented novel chaotic system, a chaotic circuit is designed. By using fractional-order operators, a controller is designed based on the state-feedback method. According to the Gronwall inequality, Laplace transform and Mittag-Leffler function, a new control scheme is explored for the whole closed-loop system. Under the developed control scheme, the state variables of the closed-loop system are controlled to stabilize them to zero. Finally, the numerical simulation results of the chaotic system with equilibrium and without equilibrium illustrate the effectiveness of the proposed control scheme.
- Chaotic system,
- circuit implementation,
- fractional-order,
- stabilization

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References(51)

References

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Highlights

● On the basis of the linear mathematical model of the two-wheeled self-balancing robot, a novel chaotic system which has no equilibrium is proposed
● A chaotic circuit is designed to demonstrate the physical realizability of the presented novel chaotic system
● On the basis of the state-feedback method, a fractional-order controller is designed by using the fractional-order theory

Fractional-Order Control for a Novel Chaotic System Without Equilibrium

doi: 10.1109/JAS.2016.7510124

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通讯作者: 陈斌, bchen63@163.com

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