Design of trajectory tracking controller for surface vessels with/without output limitations

This article creates a trajectory tracking controller for a surface vessel with or without output limitations. For the first time, a novel high-order barrier function is created to tackle the system constraints. The inequality about the created barrier function for proving the system stability is given in Theorem 1. Specifically, both systems with and without output limitations can be successfully stabilized by the control strategy developed using the created barrier function. To eliminate the impact of the system’s unknown term on trajectory tracking accuracy, an improved observer with additional items is established to compensate for the unknowable parts of surface vessels. In the framework of the backstepping method, the trajectory tracking controller for the vessel is designed based on the barrier function and the disturbance observer to prevent boundary-constraints on output from being broken. In order to demonstrate the efficacy of the presented control, numerical simulations are lastly run in Case 1, where the system’s output must be limited within the time-varying region, and in Case 2, where the system is not subject to output limits.