Global Tracking Control With Guaranteed Performance for Nonlinear Systems Driven by Delayed Inputs

This article addresses the global prescribed performance tracking control problem for uncertain nonlinear systems with delayed input and unmatched nonlinearity. By introducing a new error transformation consisting of a normalized function and a time-varying scaling function, together with an auxiliary function, we establish a robust state-feedback control scheme capable of handling the unknown and time-varying input delays without imposing any constraints on the initial condition between tracking/virtual error and performance function, leading to a global control solution to the challenging problem. Besides, the unknown delayed input is handled skillfully by the union of Lyapunov-Krasovskii functional and proof by contradiction at the final step. Furthermore, the designed controller is simple in structure and inexpensive in calculation since it does not involve any approximation tools/estimation techniques and avoids iterative computation in backstepping-like methods. It is shown that all internal signals are globally ultimately uniformly bounded, and the tracking/virtual error converges to a preassigned arbitrarily small region at a certain predefined rate. Both theoretical analysis and numerical example confirm the validity of the developed method.