“…To illustrate the effectiveness of addressing the rudder constraints and optimization via the proposed MPC algorithm, we compare the designed MPC controller with the PD controller proposed in Li et al 27 and the sliding mode method (SMC: the sliding surface is s = ψe + 0.1 tanh (0.12ψ e ) and ṡ = −0.1s). The desired waypoint: P 1 (0, 0), P 2 (4000, 0), P 3 (7000, 3000), P 4 (10,000, 3000), P 5 (12,000, 1500), and P 6 (13,500,1500). The initial states: u = 7.2 m/s, v = 0, r = 0, ψ = 0, (x 0 , y 0 ) = (0, −100 m).…”