Adaptive fuzzy backstepping super-twisting sliding mode control of nonlinear systems with unknown hysteresis

In this paper, an adaptive fuzzy backstepping super-twisting sliding mode control (AFBSTSMC) scheme is proposed for a class of nonlinear systems with unknown hysteresis, unmeasured states, and external disturbances. First, fuzzy logic systems are employed to approximate the unknown nonlinear functions of the controlled systems, and a fuzzy state observer is designed to estimate the unmeasured states. Then, combining the backstepping technique and adaptive sliding mode control with super-twisting algorithm, the AFBSTSMC scheme is proposed without constructing the hysteresis inverse. The problem of “explosion of complexity” inherent in the conventional backstepping design method is eliminated by utilizing the dynamic surface control technique. Moreover, the chattering phenomenon is significantly reduced by using the developed adaptive fuzzy super-twisting controller. It is proved that the proposed control scheme can guarantee that all the signals in the closed-loop system are semi-globally ultimately uniformly bounded and the observer and tracking errors can converge to a small domain of the origin. Finally, the effectiveness of the presented control scheme is confirmed in two examples including a numerical simulation and an inverted pendulum with unknown hysteresis actuator.