Delay-dependent adaptive dynamic surface control for nonlinear strict-feedback delayed systems with unknown dead zone

In this paper, delay-dependent adaptive dynamic surface control (DSC) is developed for a class of uncertain nonlinear time-delay systems. The considered system is in strict-feedback form with unknown dead zone. Compared with the existing results, a novel adaptive fuzzy memory state feedback controller is constructed, which relaxes the restrictions on the unknown time-delay functions and avoids the singularity problem in controller design. The unknown time delays are adaptively estimated. Design difficulties from unknown time-delay functions are overcome by using mean value theorem for differential, fuzzy logic time-delay systems, appropriate nonnegative function, and the desirable property of adaptive laws of delay parameters. A modified DSC technique is incorporated into backstepping to avoid “the explosion of complexity” problem and simplify the adaptive design procedure. By Barbalat׳s lemma, it is shown that the proposed controller can ensure that the closed-loop system is semi-globally uniformly ultimately bounded, and all the state tracking errors converge to a priori known accuracy. Finally, two simulation examples are given for showing the effectiveness of the proposed approach.