The paper studied controlling problem of an underactuated surface vessel with unknown interferences. It proved that the control problem of underactuated surface vessel can be transformed into the stabilization analysis of two small subsystems. This controller was designed by backstepping method and adaptive sliding mode, was suitable for solving the problem of the control of higher systems, can keep the system global asymptotic stability, and can inhibit unknown interference, and boundary layer can weaken the buffeting generated by sliding mode. The unknown interference was estimated by adaptive function. Finally, the simulation results are given to demonstrate the effectiveness of the proposed control laws.

With the rapid development of the modern shipping industry, the study about the controller of the underactuated surface vessel has received extensive attention. Since stabilization control problem of the underactuated surface vessel belongs to the field of nonlinear control, nonlinear control theory is the basic foundation of the underactuated stabilization control theory [

So far, underactuated ship stabilization control problem is more studied without interferences, just like [

We consider an underactuated surface vessel with simplified dynamics off-diagonal terms of the linear and nonlinear damping matrices which are ignored. Based on [

In order to design the controller conveniently, the underactuated ships model will be converted to a suitable form. Based on [

By using (

Because state transformation (

The similar proof has been given in [

According to Proposition

Block diagram of the system of (

Figure

Firstly, we consider the subsystem

We take

Secondly, we consider the whole system

We can assume the uncertain parameters

Define the Lyapunov function

Choose the control law

Finally, because the upper bound of the general object is difficult to predict, and in order to determine the uncertainties of the upper bound, we use the adaptive algorithm to estimate it.

Firstly, consider the subsystem

Assuming that lateral disturbance force decrease with time, and

Define

Secondly, consider the whole system

We assume the uncertain parameters

Choose the control law

Combining (

Finally, we use the adaptive algorithm to estimate

Firstly, we should analyze the stability of the system

We can get

So, (

From (

Secondly, system

The system shown in (

The certification process has been given in the design steps.

From field of the theory, the motion choosing sliding mode is that parameter variations and external interference have nothing to do with the systems; so, the robustness of the system using sliding mode controller is better than the general control system. But in fact, sliding mode control can cause the system chattering for the reason of noncontinuous switch; so, the boundary layer method will be introduced to weaken this vibration. Saturation function is used to replace the ideal relay functions in the appropriate boundary layer; in other words,

In order to verify that the controller is able to calm from the initial point to the origin, consider an underactuated surface vessel with the model parameters in [

Take the disturbances as follows:

In order to make ship at low speed operation, the longitudinal limited value of thrust is

From Figure

Curve of the ship’s trajectory.

Curve of ship position and heading angle variables.

Curve of ship speed.

Curve of the longitudinal force and yawing moment.

In this paper, underactuated surface vessels use the combination of adaptive sliding mode and backstepping to design the controller with the consideration of environmental disturbance and use the boundary layer method to solve the chattering problem. From the analysis of stabilization, the system is state global stabilization to the origin. The designed controller overcomes the problems of anti-to perturbation poor difficulties of the other controllers [

This work is supported by the National Natural Science Foundation of China (51209056) and the Fundamental Research Funds for the Central Universities (HEUCF 100420 and HEUCF 110430).