Approximation-based adaptive tracking of a class of uncertain nonlinear time-delay systems in nonstrict-feedback form

This paper investigates a predefined performance control problem for adaptive tracking of uncertain nonlinear time-delay systems in nonstrict-feedback form. Nonstrict-feedback nonlinearities, time-varying delays and external disturbances are assumed to be unknown. Based on the exponential decaying design functions denoting the preassigned bounds of transient and steady-state tracking errors, some variable separation lemmas are derived to design an approximation-based robust adaptive control scheme in the presence of nonstrict-feedback time-delayed nonlinearities. The proposed control system guarantees that a tracking error remains within a predesigned bound for all t ≥ 0 and converges to a preselected neighbourhood of the origin. Compared with the existing results in the literature, the main contribution of this paper is to provide a solution on the guaranteed performance control in the presence of unknown nonstrict-feedback nonlinearities related to all delayed state variables. Simulation results illustrate the effectiveness of the proposed methodology.