A nonlinear observer-based adaptive robust control approach for a class of uncertain asymmetric hysteretic systems

This article presents a robust control scheme for a class of asymmetric hysteretic systems with both parametric uncertainties and external disturbances, where an asymmetric Bouc–Wen model is adopted to represent the hysteretic behavior. A novel adaptive non-singular terminal sliding mode control methodology with hysteretic state estimation is proposed to achieve finite-time stabilization of such systems for vibration suppressions. In the proposed control framework, a hysteresis observer is constructed to capture the unmeasurable hysteretic force, and the adaptive control technique is used to accommodate the hysteretic uncertainties and unknown system parameters. Moreover, a fast terminal sliding mode controller without the singularity problem is designed to improve the robustness and dynamic performance of such systems, where the terminal sliding mode function is proposed to guarantee the finite-time convergence of the system states, and the reaching law with fractional power is constructed to accelerate the occurrence of the corresponding terminal sliding mode surface. Meanwhile, the finite-time stability of the whole closed-loop system is also analyzed. Finally, numerical simulation results deployed on a magnetorheological elastomer vibration isolation system are provided to validate the effectiveness of the proposed control algorithm.