Machine Learning-Based Autonomous Flight Vehicle Trajectory Rectification System: A Comprehensive Framework for Real-Time Path Correction

Autonomous flight systems operating in real-world environments face fundamental and multifaceted challenges in maintaining precise trajectories under complex conditions including atmospheric turbulence, wind shear, unpredictable aerodynamic effects, and sensor uncertainties. Classical guidance approaches, while mathematically elegant, rely fundamentally on simplified assumptions and fixed parameters that cannot adequately capture the nuanced, nonlinear, and time-varying reality of actual flight dynamics. This paper develops a comprehensive theoretical framework that reimagines trajectory correction through the lens of modern machine learning theory, proposing a hybrid system architecture that learns optimal guidance policies from both underlying physical principles and observed operational patterns. The architecture synergistically integrates three complementary computational components: Long Short-Term Memory (LSTM) networks for predictive trajectory forecasting, Deep Q-Networks (DQN) for optimal control policy learning through reinforcement, and Physics-Informed Neural Networks (PINNs) for enforcing physical constraints and conservation laws. I establish rigorous theoretical foundations including convergence properties under stated assumptions, Lyapunovbased stability guarantees for closed-loop operation, input-tostate stability characterizations, comprehensive computational complexity analysis for real-time implementation feasibility, and sample complexity bounds for learning efficiency. The framework addresses trajectory correction as an emergent learned capability arising from systematic exposure to diverse flight conditions while rigorously respecting fundamental physical constraints. This work provides comprehensive theoretical foundations for next-generation autonomous flight guidance systems with applications to civilian platforms including commercial delivery drones, scientific research vehicles, atmospheric monitoring systems, and emerging urban air mobility transportation networks.