Objectives  In this study, an adaptive non-singular fast terminal sliding mode rudder roll stabilization controller based on a multiple-layer recurrent neural network ( MLRNN) is proposed for the rudder roll stabilization control of an underactuated surface ship with unknown nonlinear system functions and random external disturbances.

  Methods  First, in view of the singularity and convergence problems in traditional sliding mode control, a non-singular fast terminal sliding surface is introduced, and the sliding mode control law is designed under the assumption that the ship model is known. The traditional radial basis function neural network （RBFNN） is then improved and used to approximate unknown nonlinear system functions in order to solve the problem of ship models being difficult to establish when the ship is sailing while also improving the control accuracy. The stability and finite time convergence of the system are proven by the Lyapunov theory, and the adaptive laws of the neural network parameters are derived. Finally, a numerical simulation analysis of a multi-purpose naval ship is carried out.

  Results  The results show that when the ship is under the course keeping condition, the roll reduction rate of the proposed controller is 50.41%, which is 19.2% larger than that of the non-singular fast terminal sliding mode controller (NFTSMC). When the ship is under the course changing condition, the roll reduction rate of the proposed controller is 23.46%, which is 12.59% larger than that of the NFTSMC.

  Conclusions  This method can provide valuable references for the design of underactuated ship rudder roll stabilization controllers.