that a surface vessel is a useful and suitable device for environmental surveying, seaside monitoring, military landings, and so on [1][2][3][4][5]. Despite its numerous useful applications, there are several challenging problems in the designing of tracking controller; a highly non-linear system models, stabilization, and under-actuated property, that is a system has smaller number of actuators than
ABSTRACTIn this paper, the path tracking controller for a surface vessel based on the sliding mode control (SMC) with the switching law is proposed. In order to have no restriction on movement and improved tracking performance, the proposed control system is developed as follows: First, the kinematic and dynamic models in Cartesian coordinates are considered to solve the singularity problem at the origin. Second, the new multiple sliding surfaces are designed with the SMC and approach angle concept to solve the under-actuated property. Third, the switching control system is designed to improve tracking performance. To prove the stability of the proposed switching system under the arbitrary switching, the Lyapunov stability analysis method with the common Lyapunov function is used. Finally, the computer simulations are performed to demonstrate the performance, effectiveness and stability of the proposed tracking controller of a surface vessel.