The Sliding Mode Control Of Fractional Order Chaotic Systems

The fractional order chaotic systems have become a hot topic in the recent years. The synchronization of fractional order chaotic systems is a special case of control. Due to the potential applications in secure communication and signal processing, the synchronization of fractional order chaotic systems with different dimensions, the mod-ified projective synchronization with uncertain parameters and the function projective synchronization have become the interesting and challenging problems. However, most of the existing papers discuss chaotic complete synchronization of the fractional order systems with the same dimension and certain parameters. So the main achievements are as follows:1. The synchronization of fractional order chaotic systems with different dimen-sions is investigated by means of sliding mode control and stability theorems of frac-tional calculus in this paper. Active sliding mode controller is designed to realize the synchronization of fractional order chaotic systems with different dimensions.2. This work mainly investigates modified projective synchronization of two frac-tional order chaotic systems with unknown parameters. Base on the stability theory of fractional order calculus, a controller is designed for synchronization of two different fractional order chaotic systems.3. It studies the function projective synchronization of fractional order chaotic sys-tems. According to the stability of fractional order calculus and the theory of Sliding mode control, the controller is designed.Finally, the corresponding numerical results verify the effectiveness of the pro-posed methods.