Deep Q-Network with Lagrangian Relaxation for Autonomous Aircraft Landing

Autonomous aircraft landing remains a safety critical challenge due to nonlinear aerodynamics, flight envelope constraints, and reduced control authority during the final approach and landing phase. We formulate the landing task as a Constrained Markov Decision Process (CMDP) and introduce Deep Q-Network with Lagrangian Relaxation (DQN-LR) to enable autonomous aircraft landing through throttle control. DQN-LR integrates standard Q-learning with an adaptively tuned Lagrangian penalty, encouraging the angle of attack (AoA) to remain within a prescribed safe range and guiding learning toward safe and stable landings within a predefined touchdown region. To evaluate the approach, a physics based two dimensional simulation environment is developed using the Pymunk engine, where lift, drag, and pitching-moment forces are computed from empirical aerodynamic lookup tables. Results show that the proposed DQN-LR significantly reduces AoA constraint violations while maintaining safe and stable landings compared with DQN.