# Concise Robust Control of the Nonlinear Ship in Course-Keeping Control
## 1 Introduction  
Autopilot is a piece of indispensable and vital equipment for ship maneuvering nowadays. With the improvement of navigation safety requirements and the growth of transportation demand, the requirements for autopilot are also increasing rapidly. The appearance of autopilot is a milestone in the field of navigation. It has led to the expectation to eliminate heavy manual labor and to realize automatic control in ship handling. Early mechanical autopilot can only carry out simple proportional control. It needs to select low gain for the sake of avoiding oscillation and it can only be used for low-precision course-keeping control. In the 1950s, the second generation, with a more complex and efficient electromechanical autopilot, emerged, which is well known as the PID autopilot. Its course deviation provides a correction signal to the steering equipment in an autopilot; however, the PID control method is too sensitive to high-frequency interference such as wind and waves. The \"dead zone\" nonlinear regulation is often adopted for complex steering to avoid the oscillation in course caused by high-frequency interference. Nevertheless, the dead zone often leads to the deterioration of the low-frequency characteristics for the control system, resulting in continuous periodic yawing, which will cause the deterioration of navigation accuracy, an increase in energy consumption, and the aggravation of rudder wear [1] Compared with the first generation of autopilot, the second generation of autopilot has made great progress, but it still cannot adapt to changes in the working conditions and working environment of the ship. Therefore, the steering operation is too frequent, the steering rudder angle is large, and the energy consumption and wear and tear of the steering gear are significant. In the 1970s, due to the development of adaptive control theory and the progress of computer technology, researchers began to discuss the possibility of introducing adaptivecontrol theory into ship automatic control. Under their unremitting efforts, the third generation of adaptive autopilot products was born [2; 3]. Adaptive control [4; 5] is a dynamic control method that can continuously and automatically identify the parameters of the target system, and the algorithm could adapt the ship to varying environmental conditions. Adaptive control mainly includes the adaptive PID method, the random adaptive method [6], the model reference method [2; 3], and the self-correction method [7; 8]. However, the adaptive control method is not only related to the estimated value of the cost function but also depends on the accuracy of the disturbance model established in the controller. Adaptive autopilot has achieved certain results in improving control accuracy and reducing energy consumption. However, due to the high cost of physical implementation and difficulty in parameter adjustment, especially due to the nonlinearity and uncertainty of ship motion and sea state, it is difficult to guarantee the control performance in bad weather, and sometimes it even affects the stability of the system. In recent years, with the continuous development of modern control theory and computer technology, various new control methods have been applied to the field of nonlinear ship course control, such as the feedback linearization [9], generalized predictive control [10; 11], and LQR [12]/LQG [13] methods. However, these methods have higher requirements of the control target model, and some of them have difficulty guaranteeing the control performance due to the nonlinearity and uncertainty of the ship motion system. For ship course control, it shows nonlinearity due to uncertain disturbances such as wind, wave, and current [14; 15; 16]. To solve the nonlinear and uncertain problems of ship course control, many nonlinear control technologies have been developed in ship course control.