Abstract
In this paper, the problem of stabilizing a class of fractional-order chaotic systems with sector and dead-zone nonlinear inputs is investigated. The effects of model uncertainties and external disturbances are fully taken into account. Moreover, the bounds of both model uncertainties and external disturbances are assumed to be unknown in advance. To deal with the system’s nonlinear items and unknown bounded uncertainties, an adaptive fractional-order sliding mode (AFSM) controller is designed. Then, Lyapunov’s stability theory is used to prove the stability of the designed control scheme. Finally, two simulation examples are given to verify the effectiveness and robustness of the proposed control approach.
Highlights
Fractional calculus is a mathematical topic with more than 300 years of history, its application to physics and engineering has attracted lots of attentions only in the recent years
The PC (Predictor, Corrector) method which was proposed by Diethelm et al in [30] is generally used to solve fractional differential equations (FDE)
Consider system (1) is perturbed by model uncertainty and external disturbance, and a nonlinear control input is added to the second equation of system (1), the proposed fractional-order chaotic system can be rewritten as: D q2 y g ( x, y, z ) y g ( x, y, z ) d (t ) h(u (t ))
Summary
Fractional calculus is a mathematical topic with more than 300 years of history, its application to physics and engineering has attracted lots of attentions only in the recent years. It has been found that with the help of fractional calculus, many systems in interdisciplinary fields can be described. Chaotic systems are a well-known class of complex nonlinear systems, which have several special properties, such as extraordinary sensitivity to system initial conditions, chaotic attractors, and fractal motions. The research of chaotic systems has attracted considerable attentions, for example, Gyorgyi [10] calculated the entropy in chaotic systems. Lu [13] developed a nonlinear observer to synchronize the chaotic systems. Chen et al [14,15] researched the synchronization of fractional-order chaotic neural networks.
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