On the Properties of the Backstepping Design for Marine Vehicles

A backstepping control design for marine vehicles was described in [2]. 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 possess the ability improve closed-loop response and to reject disturbance.