Model Reference Adaptive Control of Mildly Non-Linear Systems with Time Varying Input Delays - Part II
In this paper, a proof for the corollary developed for the Direct Model Reference Adaptive Tracking Control of mildly non-linear systems with unknown time varying input delays found in Model Reference Adaptive Control of Mildly Non-Linear Systems with Time Varying Input Delays - Part I is completed. The adaptive error system was developed for the 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.