Control of an Uncertain Nonlinear System with Known Time-Varying Input Delays with Arbitrary Delay Rates

A tracking controller is developed for a class of uncertain nonlinear systems with bounded external disturbances and time-varying input delay. Inspired by predictor-based delay compensators, the current result exploits a linear transformation to map the time dependent control input to a modified control input that depends on both time and a spatial variable. This transformation enables the developed controller to be applied when the delay rate is upper bounded by an arbitrarily large bound, unlike previous robust control approaches. However, unlike previous predictor-based methods, the development of a novel auxiliary error signal that includes an integral of past control values facilitates a robust control design that is applicable to uncertain nonlinear systems. A Lyapunov-based stability analysis that uses Lyapunov-Krasovskii functionals is used to prove the developed controller yields exponential convergence of the tracking error to a steady-state residual (i.e., uniformly ultimately bounded (UUB) tracking errors). Numerical simulation results are also provided to illustrate the performance of the controller for different delay rates.