Journal
IEEE-CAA JOURNAL OF AUTOMATICA SINICA
Volume 6, Issue 4, Pages 1000-1009Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/JAS.2016.7510124
Keywords
Chaotic system; circuit implementation; fractional-order; stabilization
Categories
Funding
- 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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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 Poincare 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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