Adaptive sliding mode control and its application in chaos control

The sliding motion of sliding mode control system is studied in this paper. Using the measure concept, two new quantities about the sliding motion are introduced, and a new relationship about the sliding motion is derived with the new quantities. According to this relationship, an adaptive law of the magnitude of the controller’s switching part is proposed, which can minimize the chattering phenomenon according to the predefined robust margin. To verify the effectiveness of the proposed control scheme, it is applied to Rossler system with uncertain disturbances. Simulation results show that the proposed control method can stabilize Rossler system with the magnitude of the controller’s switching part adjusted adaptively with the disturbances.