Synchronization of fractional order chaotic systems via a novel sliding mode control

In this article, a novel sliding mode control is proposed for synchronization of two fractional order chaotic systems. The proposed method uses the Radial Basis Function Neural Network(RBFNN) and proportional-integral(PI) parallel control to replace the traditional switching law of adaptive sliding mode control(ASMC). The advantages of the control method are as follows: firstly, the continuous nonlinear approximation capability of RBFNN ensures the system will not produce chattering since eliminating chattering is a key study point of ASMC; secondly, the superior self-learning ability of RBFNN makes it possible for the control systems to improve the overshoot and decrease the settling time; finally, the proposed method introduces the PI parallel control to overcome the disadvantage of local convergence of RBFNN. The asymptotic tracking of the states of the response system and the drive system is proved via the Lyapunov-based stability analysis. Considering the dimensions of the response system and drive system are not always same under normal conditions, the simulation results of two types are presented to validate the effectiveness of the method.