Adaptive fuzzy tracking control for underactuated surface vessels with unmodeled dynamics and input saturation

This paper investigates the tracking control of the underactuated surface vessel (USV) with the off-diagonal inertial matrix, and under the influence of unmodeled dynamics as well as the constraint of input saturation. With the fuzzy logic systems (FLSs) accounting for the uncertainties, we present an adaptive fuzzy state-feedback control scheme with the minimum learning parameters (MLPs) of the FLSs. Based on the conventional USV model described in three degrees of freedom (DOF), an improved model is established at first, which involves the terms of dynamic disturbances generated by the unmodeled dynamics of the indecisive motions. Then, the off-diagonal inertial matrix is released by restructuring the kinematic loop of the improved model, and the backstepping approach is employed through the control design. To solve the underactuated problem, the tracking error in the sway motion is restructured by adding an adaptive compensating variable and further allocated to the actuated motions. The K_∞ functions are structured in the control laws to offset the dynamic disturbances. The Gauss error functions are employed to approximate the uncertainties of the input saturation, which are described by the continuous control inputs with the bounded multiplicative gains. Via the small-gain theorem, the resulting closed-loop system is proved to be ultimately bounded. Finally, a simulation example is carried out to validate the effectiveness of the developed scheme.