Fractional-order control for a novel chaotic system without equilibrium

• Published in: IEEE/CAA journal of automatica sinica Vol. 6; no. 4; pp. 1000 - 1009
• Main Authors: Shao, Shuyi, Chen, Mou
• Format: Journal Article
• Language: English
• Published: Piscataway Chinese Association of Automation (CAA) 01.07.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Chaos theory; Chaotic communication; Circuit design; Closed loop systems; Computer simulation; Control systems; Control systems design; Equilibrium; Feedback control; Laplace equations; Liapunov exponents; Mathematical model; Mathematical models; Operators (mathematics); Poincare maps; Realizability; Robots; State variable; Synchronization
• ISSN: 2329-9266; 2329-9274
• DOI: 10.1109/JAS.2016.7510124

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.