Tracking control of bilinear control system with disturbance using backstepping-sliding mode control

The control design in a nonlinear control system depends on the model. A disturbance function in the system will result in unpredictable system dynamics. The most straightforward strategy is changing the nonlinear system into a linear system. In this article, we discuss the application of the backstepping method combined with sliding mode control to control the output of a disturbed bilinear control system. The bilinear control system is transformed into the normal form using input-output feedback linearization. We assume the system has a relative degree equal to the system dimension so that the system can be exactly linearized, and the disturbance function only affects the dynamics containing the control function. Control design in normal form is carried out using the sliding control method. The sliding control method is modified by setting the Lyapunov function in the Backstepping process. The article ends with some examples to demonstrate the proposed method’s performance. The results evidence that the proposed control successfully brings the output to the trajectory and copes well with disturbances.