Theoretical Analysis and Stability Assessment of Machine Learning-Enhanced Numerical Solvers for Nonlinear UAV Flight Dynamics.

Abstract:

Accurate numerical modelling of nonlinear unmanned aerial vehicle (UAV) flight dynamics remains a critical challenge, particularly under strongly nonlinear operating conditions where classical solvers require small integration step sizes to maintain stability. This study presents a hybrid numerical framework that integrates a fourth-order Runge-Kutta (RK4) solver with a learning-based correction mechanism to enhance accuracy while reducing computational cost. The proposed approach is analytically investigated in terms of numerical error decomposition, convergence behaviour, and stability characteristics. A multilayer perceptron (MLP) is employed to learn the residual numerical error and provide corrective updates while preserving the underlying physical structure of the system. Numerical validation is performed using flight trajectory datasets representing realistic UAV operations. The results demonstrate that the proposed framework achieves a Root Mean Square Error (RMSE) of 1.82 × 10⁻³ rad in pitch angle prediction while reducing computational cost by approximately 38% compared to the baseline RK4 solver. The findings confirm that hybrid learning-based numerical schemes can provide a practical balance between accuracy, efficiency, and numerical robustness.