Adaptive course keeping control for rudder angle constraint nonlinear ship systems with dead-zone input and uncertain control coefficients

• The Nussbaum-type function is used to deal with the problem of direction-uncertain control coefficients. • The partial state constraints are discussed in the ship course keeping control systems. • According to the characteristics of ship and the practical steering habits, the BLF is applied to restrict the rudder angle. This paper proposes an adaptive course keeping control algorithm based on Nussbaum functions and barrier Lyapunov function (BLF), targeting the complexity and uncertainty of ship navigation conditions and rudder angle constraints and dead-zone input existing in the course keeping process. Initially, the Nussbaum functions are incorporated into the control scheme to address the issue of direction-uncertain control coefficients, thereby avoiding the singularity problem of the controller. Subsequently, a BLF is utilized to constrain the rudder angle, reducing the steering frequency and energy consumption of the steering gear and making the control actions more consistent with the operational habits of the crew. Meanwhile, the radical basis function neural networks (RBF NNs) are employed to approximate uncertain parameters, while the dynamic surface control (DSC) is applied to simplify the computation process and reduce controller complexity. Then, rigorous mathematical proofs demonstrate that all system signals are semi-globally ultimately uniformly bounded (SGUUB) under the proposed control algorithm and the rudder angle constraints are maintained within a predefined compact set. Finally, simulation examples validate the effectiveness of the proposed scheme.