Synchronization of chaotic system with adaptive transfer function sliding mode method

Genesio system was taken as an example to show the design process of synchronization of chaotic system with reduced number of active inputs which can be transferred into a control problem of special second order system. A kind of adaptive transfer function method is integrated with sliding mode control method to solve the control problem of second order system with double control directions. And sliding mode method can reduce system order and make the design process more simple. But double control direction will caused a derivative of control problem, which is difficult to solve with traditional method. So a kind an equivalent transfer function method is proposed to cope it. Also, the proper parameters of transfer function are estimated by adaptive methods. At last, detailed simulation result is done to testify the rightness of the proposed method and simulation shows some problems which is caused by the adaptive method that the stable condition for transfer function can not be guaranteed. Also, the simulation of the complex chaotic synchronization was realized with the proposed adaptive transfer function method, so the rightness of this novel method was totally verified.