Nonlinear Gains Recursive Sliding Mode Dynamic Positioning of Ships with Uncertainties and Input Saturation

To address dynamic positioning (DP) challenges encountered by ships navigating amid unknown model parameters, environmental disturbances, and input saturation, this study proposes a nonlinear gains recursive sliding mode (RSM) DP control law. Within this control framework, an RSM strategy is devised, leveraging variable-gain technology to enhance DP system control performance. A variable-gain adaptive radial basis function (RBF) neural network is employed for real-time online training to approximate the unknown ship model. Simultaneously, an auxiliary dynamic system is incorporated to deal with input saturation. Furthermore, a robust control item is implemented to counteract the influence of RBF neural network approximation errors and external disturbances on the DP system. By constructing an appropriate Lyapunov function, it is proven that all signals in the DP closed-loop control system are uniformly ultimately bounded. Finally, simulation results demonstrate the ship DP system’s rapid response and high accuracy under the proposed control law, along with an enhanced ability to reject environmental disturbances.