Synchronization of two different chaotic systems using RISE feedback

In this paper, RISE (robust integral of the sign of the error) feedback controller is considered to synchronize two different chaotic systems. This control scheme is inspired from sliding mode technique while in comparison with sliding mode controllers; Rise reduces the chattering phenomena. According to especial structure of Rise feedback; this controller can control plants with different relative degree. Also the control law of the RISE feedback depends on measurement of the state variable and this characteristic is one of the most important differences that demonstrate the new type of control design. In order to present the performance of the Rise feedback in synchronization, Pendulum and Duffing chaotic system have been considered as a master and slave system respectively. The capability of the proposed method to control uncertain 2nd order nonlinear system is rendered with lyapunov stability analysis and the performance of this scheme is compared with 2nd order sliding method and PD controller. The simulation results endorse the proficiency of the RISE feedback strategy

Keywords:

Synchronization , Chaos , RISE (robust integral of the sign of the error) feedback , twisting algorithm , PD controller , Pendulum , Duffing