Extension sliding mode control for nonlinear systems

This paper presents a novel extension controller based on a scheme for sliding mode control. The control strategy of the proposed controller is classified in two parts. One is the equivalent control of sliding mode control, which can be directly obtained from the knowing nominal system. The other is the well-known robust control, which is used to compensate for the system uncertainty and external disturbance. Integrating the essential concept of extension set theory with the sliding mode control, we can easily realize the robust extension controller. In this study, we first organize a basic extension controller without any specific expert knowledge about the controlled system. According to the determined extension characteristic functions, the functions supervise system states' information under control. A set of parameters, which will be adapted using adaptation strategy, is incorporated into the extension controller such that a robust control, also called a hitting control, is established to guarantee the system's robust stability. As a result, the proposed extension controller is stable in the Lyapunov sense. Finally, we use the proposed extension controller to control a nonlinear system to verify its effectiveness and ability.