Command Governor-Based Adaptive Control

Abstract

Even though an important prerequisite for an adaptive controller is the ability to adapt fast in the face of large system uncertainties, fast adaptation with high-gain learning rates can be a serious limitation due to the fact that it can possibly yield to high-frequency oscillations especially during the transient system response. Therefore, achieving fast adaptation with low-gain learning rates and predictable transient and steady-state system response is the challenge for the adaptive control theorist today. To that end, we introduce a novel command governor architecture for adaptive stabilization and command following. Specifically, the proposed command governor is a linear dynamical system which adjusts the trajectories of a given command in order to follow an ideal reference system both in transient time and steady-state without resorting to high-gain learning rates in the adaptation law. It is shown that by choosing the design parameter of the command governor, the controlled nonlinear uncertain dynamical system can approach a Hurwitz linear time-invariant dynamical system with L∞ input-output signals. This provides a systematic framework for verification and validation of adaptive control systems and the proposed command governor can be used in a complimentary way with many other approaches to adaptive control.