Adaptive Control of Nonlinear Systems with Unknown Delays and Persistent Disturbances

Abstract

In this paper, we develop a Direct Model Reference Adaptive Controller for nonlinear systems with unknown delays. This controller can also reject bounded disturbances of known wave form but unknown amplitude, e.g. steps or sinusoids. We prove an infinitedimensional version of the Lyapunov-Barbalat Stability Theorem, and use it to show that the controller produces global asymptotic tracking with bounded controller gains when the delay-free open-loop plant is almost strictly dissipative and the internal delay terms satisfy a matrix inequality. The adaptive controller has no knowledge of the delay. We derive results for linear systems as a corollary. An illustrative example is provided.