Fixed-time backstepping control for overturn prevention of a trans-media vehicle during high-speed water entry

The stable control of a trans-media vehicle during high-speed water entry is crucial for mission success. However, drastic state variations during the control process can easily trigger vehicle overturn, leading to system instability and even safety hazards. It is therefore imperative to impose strict state constraints in the controller design. Furthermore, composite uncertainties of the system can severely degrade control performance. To address these challenges, a fixed-time backstepping control scheme incorporating the overturn-prevention condition is proposed in this paper. Based on the geometric relationship between the vehicle and the cavity, the state constraint boundary for overturn prevention during the high-speed water entry process is established. By introducing a nonlinear transformation function, the control problem with full-state constraints is converted into ensuring the boundedness of error-dependent functions, thereby eliminating the dependence on feasibility conditions. A fixed-time disturbance observer is designed to estimate and compensate for the lumped disturbance, guaranteeing that the estimation error converges within a fixed time independent of initial conditions and enhancing system robustness. On this basis, a fixed-time backstepping control strategy is developed by incorporating a novel nonlinear tracking differentiator. Rigorous theoretical analysis proves that all closed-loop signals satisfy the state constraints, and the state errors converge to a small neighborhood of the origin within a fixed time. Simulation results demonstrate that the proposed method effectively prevents overturn and exhibits significant superiority in both transient performance and steady-state precision.