Long-Horizon Stable UAV Dynamics Forecasting With Neural Lyapunov Functions and Spatial–Temporal Linear Transformer

Reliable long-horizon dynamics prediction for UAVs is crucial for mitigating collision risks as urban air mobility expands rapidly. However, current prediction methods suffer from distribution shift and error accumulation due to complex nonlinear dynamics and noisy data. To address these issues, we propose a stability-guaranteed dynamics modeling (SGDM) method which integrates a spatial-temporal linear Transformer (STLT) with a neural Lyapunov function (NLF). The STLT enables efficient long-horizon dynamics prediction while eliminating error accumulation and distribution shift through spatial-temporal decoupled multi-head attention, linear-complexity attention, and a non-autoregressive decoder. The NLF enforces global exponential stability by restricting predictions to a Lyapunov stable subspace. Then, a stability-constrained optimization algorithm is proposed to optimize STLT and NLF jointly, thereby assuring both prediction accuracy and stability. Experimental results on helicopter and quadrotor datasets demonstrate that SGDM outperforms state-of-the-art models, reducing RMSE by 48-71% and accelerating inference by 14-45%. This work effectively bridges data-driven learning with Lyapunov stability theory, providing reliable long-horizon dynamics prediction for safety-critical UAV operations.