## 1 Introduction  
Currently, the shipping industry is vigorously developing, and ship transport has become one of the most effective and economical transportation methods to fulfill the trading of bulk goods between regions and countries, so the study of ship control has vital value [1, 2, 3, 4]. Ship control is an important subject, as well as the application of control theory in the area of navigation technology research. Along with the evolution of control theory, various kinds of advanced control technologies and control theories have been applied to the design of ship controllers and have achieved ideal control effects [5, 6, 7, 8, 9, 10, 11]. Backstepping-based adaptive control technology emerged in the 1990s as a useful tool for analyzing and designing the controller of nonlinear systems. It has a relatively complete adaptive control theory and a nonlinear robust control theory for systems with uncertain parameters, and this method has been widely used in various works on ship operation control. It is important to note that this technique has the precondition that the controlled system functions are available or can be expressed as the product of uncertain constants and known functions. However, the marine environment is complex and changeable, and the ship mathematical model is also uncertain. At this time, when the ship control model cannot meet these restrictions, the above control design method will no longer be applicable. Therefore, many experts in the control field began to explore new technologies to solve this problems. Intelligent control technology (neural network or fuzzy logic system (FLS)) brings new research ideas to solve this kind of problem. The development of adaptive intelligent control technology not only promotes the development of the nonlinear control field, but also brings new hope for dealing with complex problems in ship control systems [12, 13, 14, 15, 16]. For example, using intelligent control technology, the adaptive output feedback control problem of an intelligent ship autopilot systems was addressed in [12]. It can be easily found that, in the backstepping design, the drawback of the \"explosion of terms\" is inescapable, and this greatly increases the difficulty and complexity of the calculations; thus, the resulting control tactics are sometimes not easy to apply in engineering. In addition to the usual methods, such as dynamic surface control (DSC) [17; 18], it can be seen that the above problem was similarly managed by the tracking differentiator (TD) technique in [19; 20], and the expected control target was successfully achieved. The TD technique has been proven to be a good tool, but few results on stochastic systems, even on ship control, have been reported. This is an interesting and meaningful work, which aroused our research interest. In practice, the structure of a ship control system is intricate and changeable, with highly nonlinear characteristics and model uncertainty. In the control process, the ship control system is also susceptible to various external and stochastic noises, such as weather change, water velocity, and draft depth in complex sea conditions. It is necessary to consider the stochastic noise in the ship control performance when establishing the system mathematical model, as the requirements of actual engineering technology on system accuracy become higher and higher. The control of stochastic systems has become a vibrant research area recently, and numerous theoretical and applied works have been published [21; 22; 23; 24]. Despite all these research achievements, however, there are few research results on the problem of ship control systems with stochastic noise at present [25; 26; 27], and these results ignore the switching mechanism in the analysis and control design. The switching control problem under different wind levels and water velocities needs to be considered.