A novel asymmetric barrier Lyapunov function-based fixed-time ship berthing control under multiple state constraints

Abstract

The construction of an asymmetric barrier function with internal security set, while ensuring its invariance in the presence of interference, is a challenging task to achieve stability and security. In this paper, a translation transformation is used to construct a novel asymmetric Barrier Lyapunov Function. To the best of our knowledge, this is the first designed continuously differentiable barrier Lyapunov function (BLF) of this type. A new adaptive sliding mode control (SMC) method based on asymmetrical BLF is proposed for uncertain external disturbances. The robust control method can ensure the safety performance in the presence of model uncertainty with bounded tracking error of the ship trajectory and velocity. Its fixed-time convergence is then proved by the Lyapunov theory. The results show that it has stronger anti-interference ability in bad sea conditions, better robustness, and concise form. In addition, the system can deal with unknown disturbances, ensure the safe navigation, and keep the good tracking of the route under wind and current disturbance due to random sea conditions.