Abstract
To address the path following of underactuated unmanned surface vehicles (USVs) under external disturbances with computational efficiency, this paper proposes an efficient algebraic model predictive control (e-AMPC) framework with disturbance compensation. A nonlinear disturbance observer (NDOB) is embedded into the prediction model, and a variable coincidence-point strategy is adopted to reduce the computational load. The cascade system, composed of the e-AMPC controller and the NDOB, is analyzed as a whole, and a Lyapunov-based proof is provided to establish input-to-state practical stability under bounded disturbances. Extensive simulations verify the superior path-following performance and accurate disturbance estimation, achieving an approximately 74% reduction in computation time compared with conventional MPC. The simulations also quantitatively reveal the influence of prediction-point distribution, weighting matrices, and observer gain on disturbance rejection and tracking accuracy. These guidelines significantly enhance the engineering practicality and reliability of the proposed controller.