Model Reference Adaptive Control of Mildly Non-Linear Systems with Time Varying Input Delays - Part I
In this paper, we develop a Direct Model Reference Adaptive Tracking Controller for mildly non-linear systems with unknown time varying input delays. This controller can also reject bounded disturbances of known waveform but unknown amplitude, e.g. steps or sinusoids. In this paper a robustness result is developed for DMRAC of mildly non-linear systems with unknown small constant or time varying input delays using the concept of un-delayed ideal trajectories. We will show that the adaptively controlled system is globally stable, but the adaptive tracking error is no longer guaranteed to approach the origin. However, exponential convergence to a neighborhood can be achieved as a result of the control design. A simple example will be provided to illustrate this adaptive control method. The proof of the corollary for the application and further examples are provided in the paper: Model Reference Adaptive Control of Mildly Non-Linear Systems with Time Varying Input Delay - Part II.