Adaptive prescribed-time control for stochastic nonlinear systems over infinite horizon: A dynamic threshold strategy with application to ship maneuvering systems.

This paper studies the prescribed-time tracking control problem with output constraints for stochastic nonlinear systems over an infinite horizon, motivated by ship maneuvering dynamics. The steady-state tracking accuracy of existing methods is uncertain due to unknown system parameters, which may fail to meet high-precision requirements. To address this issue, an adaptive prescribed-time control framework based on a dynamic-threshold mechanism is developed, which extends the time-accuracy regulation idea to output-constrained stochastic nonlinear systems. A time-varying asymmetric barrier Lyapunov function (BLF) is constructed to enforce output constraints. By incorporating a finite-time command filter and neural networks, the proposed approach alleviates the explosion of complexity in backstepping and approximates unknown nonlinearities. Simulation studies based on a ship maneuvering model demonstrate that the closed-loop system is bounded in probability. Moreover, the system output converges to a prescribed precision neighborhood within the specified time while the output constraints are satisfied at all times.