Adaptive fuzzy output feedback control of MIMO nonlinear uncertain systems with time-varying delays and unknown backlash-like hysteresis

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of multi-input and multi-output (MIMO) nonlinear systems with time-varying delays and unknown backlash-like hysteresis. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and an adaptive fuzzy state observer is designed to estimate the unmeasured states. By utilizing the adaptive fuzzy observer, and combining the fuzzy adaptive control theory with backstepping approach, an adaptive fuzzy output feedback control approach is developed. The proposed control approach can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SUUB), and the observer error and tracking error are proved to converge to a small neighborhood of the origin. Two simulation examples are included to illustrate the effectiveness of the proposed approach.