Efficient Algebraic Model Predictive Control with Nonlinear Disturbance Observer for Unmanned Surface Vessels Path Following

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.