Research On Robust Synchronization Of Fractional-order Chaotic Systems

Chaos is an extremely complex nonlinear dynamic behavior which is widely exists in nature. Since it has many excellent properties such as the extreme sensitivity to the initial values and parameters, the intrinsic randomness and so forth, chaos system will be widely used in many fields, especially applied in the field of secure communication. As a generalization of the general form of the integer-order chaotic system, fractional-order chaotic system not only widely exists in many engineering fields, but also has a better application prospect in the field of secure communication due to its dynamic characteristics associated with the system order, has a certain historical memory effect and more complex chaos characteristics. Research on synchronous control for the fractional-order chaotic system has become a hot topic of study on chaos. This paper focuses on the synchronization of fractional-order chaotic systems in the condition of uncertain parameters, disturbances and communication time-delay.First, chaos synchronization of a class of fractional-order chaotic systems in the condition of system parameters partly unknown or completely unknown and uncertain disturbances is discussed in this part. A novel adaptive controller and updating law are designed. The theoretical proof and numerical simulations are presented to verify the designed control methodSecond, we investigate the hybrid projective synchronization between different fractional-order chaotic systems in the presence of system parameter uncertainty and unknown bounded external disturbances. Based on adaptive control theory and switch control theory, we design an adaptive controller and the adaptive updating law, to realize the robustness hybrid projective synchronization between two different fractional-order chaotic systems in the same dimension or different dimensions.Finally, the hybrid projective synchronization of two different fractional-order chaotic system with time-delay and uncertain random perturbation is discussed. Adaptive sliding mode control method is proposed. Stability is analyzed and two numerical simulations verify the effectiveness of the control method for the design.