Fixed-Time Stable Fault-Tolerant Control of Underactuated Hovercraft via Physics-Informed Neural Adaptation

Abstract

This study addresses the trajectory tracking control problem for an underactuated hovercraft subject to additive bias and multiplicative loss-of-effectiveness thruster faults under environmental disturbances. In these systems, actuator degradation structurally breaks the differential flatness mapping, driving nominal controllers to generate control actions that induce severe actuator saturation and cause instability. To resolve this challenge, a hierarchical physics-informed neural adaptive control (PINAC) framework is proposed. First, a gated-recurrent-unit physics-informed neural observer (PINO) is designed to isolate thruster faults from exogenous hydrodynamic disturbances. Second, a constrained Safe-TD3 reinforcement learning agent functions as a supervisor, computing an online dilation factor to slow down the mission timeline, thereby reconfiguring the reference trajectory to accommodate degraded actuator boundaries. Third, a low-level non-singular terminal sliding mode (NTSM) controller is implemented as a tracking-guarantee layer. Unlike classical asymptotic schemes where convergence is only achieved as time approaches infinity, or finite-time controllers where the settling time depends on the initial state, the proposed PINAC framework guarantees practical fixed-time stability, ensuring that the settling-time bound is independent of initial conditions. Simulation results demonstrate that the designed controller prevents actuator saturation, provides smooth trajectory adjustment, and reduces tracking errors under severe composite faults.