A backstepping‐based low‐and‐high gain design for marine vehicles

Abstract

Abstract A backstepping control design for marine vehicles was described in ( Marine Control Systems: Guidance, Navigation and Control of Ships, Rigs, and Underwater Vehicles . Marine Cybernetics AS: Trondheim, Norway, 2002). Under a backstepping feedback law, global asymptotic stability of the closed‐loop system can be shown under the assumption of unlimited actuation. This paper addresses the issues that arise in the implementation of a backstepping feedback law by saturating actuators. First, for a given backstepping feedback law, an estimate of the domain of attraction is given for the resulting closed‐loop system under actuator saturation. A high gain component is then constructed and augmented to the original backstepping feedback law. This additional high gain component is shown not to shrink the estimate of the domain of attraction but to possess the ability to improve the closed‐loop response and to reject disturbance. Copyright © 2008 John Wiley & Sons, Ltd.