Simplified filtering‐based adaptive fuzzy dynamic surface control approach for non‐linear strict‐feedback systems

Abstract

In this study, the problem of filtering-based adaptive fuzzy control is investigated for non-linear strict-feedback systems with unmeasured states. An input-driven filter is designed for estimating the unmeasured states. By exploiting the bound of system output, an upper bound of filtering error is obtained and it is further optimised by solving a set of linear matrix inequalities. Then under the framework of backstepping design technique incorporated by dynamic surface control approach, and by using the obtained upper bound, a novel adaptive fuzzy dynamic output feedback control approach with one adaptive parameter is developed. It is shown that all the signals of the closed-loop system are bounded, while the tracking error converges to a small neighbourhood of the origin. The main advantages of the proposed approach are that choice of design parameters is independent of the order of system such that closed-loop system can achieve a better tracking performance, and compared with the existing results, the controller has a much simpler structure embodied in its form, adaptive parameter and membership functions of fuzzy logic systems. Finally, two examples are given for showing the effectiveness of the proposed approach.