Simple adaptive output-feedback control of non-linear strict-feedback time-delay systems

Abstract

An adaptive output-feedback control approach is proposed for uncertain non-linear systems with unknown time delays in strict-feedback form. A linear observer is designed to estimate unmeasurable state variables. In contrast to the existing controllers for strict-feedback systems, the adaptive control design using only single fuzzy approximation (SFA) is presented. In the controller design procedure, unknown non-linear functions including unknown non-linearities caused by compensating time-delay functions are derived to design virtual controllers. They are not approximated by using fuzzy logic systems at each step of the backstepping design, but just passed down to the next step. Finally, a lumped unknown non-linear function including non-linearities of observer error dynamics is defined at the last step and estimated by SFA in order to design the actual control law. Thus, the actual control law using SFA can be implemented, without calculating virtual control laws. Compared with existing output-feedback control approaches for strict-feedback time-delay systems, the proposed control system has a relatively simple structure in that it overcomes the problem of using multiple approximators as well as the problem of calculating the repeated differentiations of virtual controllers. In addition, we show that all signals in the closed-loop system are uniformly ultimately bounded and the tracking error converges to an adjustable neighbourhood of the origin.