Output-feedback adaptive fuzzy control for a class of non-linear time-varying delay systems with unknown control directions

In this study, an adaptive fuzzy control scheme is proposed for a class of non-linear systems with unknown discrete and distributed time-varying delays via dynamic output-feedback approach. Unlike the system with only one unknown control coefficient, the so-called high-frequency gain, the system we will consider is more general. During the controller design procedure, novel Lyapunov-Krasovskii functionals are introduced to compensate for the unknown time-varying delay terms and all unknown functions are lumped into a suitable unknown function which can be approximated by only one fuzzy logic system (FLS). The main advantages of this study are that (i) the output-feedback adaptive fuzzy controller can dispose a class of non-linear systems with unknown time-varying delays, in which the virtual control coefficients are all unknown, (ii) it does not need to know the time delays and their upper bounds and (iii) only one parameter needs to be adjusted online in controller design procedure, which reduces the online computation burden greatly. It is proven that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded, whereas the tracking error converges to a small neighbourhood of the origin. Finally, simulation results are provided to show the effectiveness of the proposed approach.