| Fractional calculus is a branch of mathematical analysis, which contains arbitrary order derivative and integral research and application. As a basic tool for modeling, fractional calculus is more appear to the reality. So far, researchers have focused on the synchronization of the integer order chaotic system, and quite much results has been provided. However, the attention on fractional order system were fewer because of its complexity. The methods of synchronization of integer order can also be applied to frantional order system. Here, we considered the impulsive method for its good robustness and anti-noise ability. Besides, the fuzzy method is applied to remove the influence of nonlinear part of the system.In this paper, based on the stability theory of fractional order and fractional Lyapunov second method, we get the condition and conclusion to realize synchronization of fractional order chaotic system with certain and uncertain parameters. Then, appropriate fractional order chaotic system were selected to do numerical simulation which vertified the effenicence of our conclusion. When the synchronization of fractional order chaotic systems with parameters is determined:Firstly, the classical fractional order driven and response systems are selected. Then, plus impulsive control respectively and get two impulsive chaotic systems. Secondly, based on the classic T-S fuzzy rules for two pulses fuzzy elimination of the nonlinear parts of the two impulsive chaotic system. And then get the error system based on the two fuzzy impulsive systems. Finally, through the method of single point of fuzzy, reasoning and weighted average defuzzification to obtain the final error system. Then the Lyapunov second method is used to realize the synchronization of the fractional order error system. Some properties of the fractional differential equations and fractional calculus is also applied in the proof process. Finally, two chaotic system are selected to do numerical simulation which vertified the effenicence of our conclusion. When the synchronization of fractional order chaotic systems with parameters is uncertain:The Lyapunov second method is used to judge the stability of the impulsive fuzzy synchronization of two fractional order chaotic systems under the condition of parameter uncertainty. The research process is similar to the synchronization of fractional order chaotic systems with parameter determination. Firstly, select the drive system and response system. Compared with the parameters determined system, the parameter uncertainty was considered and generally very small due to the boundedness of chaos, t. Then adding impulsive control and eliminating the nonlinear parts by fuzzy method. Then get the error system by two impulsive fuzzy chaotic system. Finally through a single point of fuzzy, reasoning and weighted average defuzzification, we obtained the final error system. Further application of the second method of Lyapunov for constructing suitable controller, the coefficient of controller to meet the adaptation rate. Discussed the conditions to achieve synchronization. Finally, choose the appropriate chaotic system experiments to prove that the validity of the conclusions drawn. |
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