Adaptive nonlinear tracking control of an underactuated nonminimum phase model of a marine vehicle using ultimate boundedness

In this paper, an adaptive nonlinear tracking controller for an underactuated nonminimum phase model of a marine vehicle is derived. The result is kept flexible enough, throughout its derivation, to be applicable to a large variety of marine vehicles. The characteristics of the dynamic model are such that solving the tracking problem is non-trivial. Specifically, we consider a propulsion system composed of either a thruster and a rudder, or a vectored thruster, which provides two independent control commands and three degrees of freedom, with an overall unstable zero-dynamics. The tracking problem dealt with in this paper is solved using a backstepping approach, as well as a technique derived from dynamic surface control theory and the notion of ultimate boundedness. The tracking problem is first solved assuming full knowledge of the geometric and hydrodynamic coefficients appearing in the vehicle's model. The control law is then modified into an adaptive one. Computer simulations are presented to illustrate the performances of the final control algorithm.