A novel adaptive-impulsive synchronization of fractional-order chaotic systems**Project supported by the National Natural Science Foundations of China (Grant Nos. 11161027 and 11262009), the Key Natural Science Foundation of Gansu Province, China (Grant No. 1104WCGA195), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20136204110001).

Abstract

A novel adaptive–impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors’ bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive–impulsive control scheme.