# Model Based Robust Predictive Control of Ship Roll/Yaw Motions with Input Constraints
## 1 Introduction  
For safe sailings and operations in the ocean, large ships often encounter uncertain situations, such as supply difficulties, unknown sea conditions and hidden risks in the operation of marine equipment, which may affect the ship safety during the sailing [1]. Therefore, it is of great significance for large ships, especially containers, to predict and optimize the performance of real marine motion system with wave disturbance, including optimizing ship motions as well as actuator actions and reducing the saturation rate of the actuators. In particular, the constraints of actuators of the rudder-fin joint system draw much attention in the study field of ship safe sailing [2; 3; 4; 5; 6; 7]. The maximum angle of the fin stabilizers/rudder is usually limited, namely saturated, which may cause dynamic stall and even instability of the system risking severe accidents [8]. Moreover, the input constraints of the actuators are also reflected in the input delay characteristics of the fin stabilizer driving system, which further deteriorates the control performance. Many novel methods, including relevant nonlinear control, have been applied to ship motion control tentatively [3; 9]. In recent years, with the development of various advanced control algorithms, the feedback linearization and other nonlinear control methods are applied for ship autopilot control. [PERSON] and [PERSON] employed the nonlinear variable structure robust control method in fin stabilizer control [10]. [PERSON] and [PERSON] applied the model predictive control to the fin stabilizer control to prevent the occurrence of dynamic stall [4]. In addition, the rise of intelligent control methods has attracted a large number of scholars [11; 12; 13]. Some achievements of rudder roll reduction are included in [3; 14]. The most important of these achievements is to adopt the modern control technology based on the nominal state space model to deal with the problems of rudder roll reduction. The main control method is LQG and its integrated/improved control approaches [15; 16; 17; 18; 19]. Additionally, [PERSON] applied\(H_{\infty}\) control to rudder roll reduction [20]. Although the modern control methods improve the efficiency of roll stabilization, the effect of high and low encounter frequency is still not ideal. Most nonlinear processing methods based on strict feedback nonlinear system have the advantages of fast response, good convergence and high accuracy, and they achieve certain control effect. However, it is also found that the conventional nonlinear control methods for MIMO system have the following shortcomings: the design process is complex, and the adjustment of control parameters is difficult; the performance indexes set by users cannot be optimized online and real-time; constraints cannot be explicitly considered, such as state constraints, actuator input constraints (including saturation and delay characteristics of actuators), which may cause the degradation of the control performance. The above issues motivate the studies of deploying model predictive control (MPC) in ship motion control. The method has been widely used in process industries [21; 22; 23] due to its excellent capacity of dealing with multivariables and various constraints. In recent years, abundant results have been reported in different application fields, such as advanced manufacturing, energy storage, electrical engineering, and so on [24; 25; 26]. A significant feature of MPC is the receding horizon fashion, and the optimization problem is solved at each time instant to determine the control inputs. Both fin roll reduction and rudder roll reduction are faced with the problems of complex modeling and controller failure caused by the change of sailing states. Abundant results on MPC addressing ship control have been reported concerning the above issues. ODA proposed a method based on autoregressive model that can automatically identify models online [7].