Adaptive Tracking Control of Linear Systems with Unknown Delays and Persistent Disturbances (or Who You callin' retarded?)

Abstract

In this paper, we develop a Direct Model Reference Adaptive Tracking Controller for linear systems with unknown delays, sometimes known as retarded equations. This controller can also reject bounded disturbances of known wave form but unknown amplitude, e.g. steps or sinusoids. We prove that the controller produces global asymptotic tracking with bounded controller gains when the delay-free open-loop plant is almost strictly positive real (equivalently, is minimum phase and has CB positive definite) and the internal delay terms satisfy a linear matrix inequality. The adaptive controller has no knowledge of the delay. An illustrative example is provided.