Coupled-variable-based tracking control for state-constrained surface ships under external disturbance

This paper investigates the tracking control problem for surface ships subject to position and velocity tracking error constraints, and unknown environmental disturbance. To achieve this, a disturbance observer is designed to estimate and compensate for external disturbance. Furthermore, a coupled-variable constraint is introduced, in which an auxiliary error signal is constrained to simultaneously constrain both position and velocity tracking errors. Meanwhile, the relationship among these three variables is rigorously analyzed. And the pre-specified constraints can be satisfied as long as the barrier Lyapunov function (BLF) remains bounded. Compared with the methods based on BLFs or Nonlinear Mapping to constrain position and velocity tracking errors, the proposed strategy only employs a single constraint condition to simultaneously limit both errors. Moreover, this technique eliminates the need for recursive process and feasibility condition verification, thereby significantly simplifying the control design. The effectiveness of the proposed control algorithm is validated through simulations conducted on the CyberShip II model.