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Volume 6 Issue 4
Jul.  2019

IEEE/CAA Journal of Automatica Sinica

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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

Fractional-Order Control for a Novel Chaotic System Without Equilibrium

doi: 10.1109/JAS.2016.7510124
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

More Information
  • 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.

     

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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

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