Computationally Efficient Bayesian Model Predictive Control for 4-D Flight Trajectory Tracking Under Windy Conditions

Accurate 4-D trajectory tracking can improve trajectory predictability and further enhance the efficiency of air traffic management (ATM). However, the tracking accuracy is inevitably affected by uncertainties arising from wind. To maintain tracking performance, a novel Bayesian model predictive control (MPC) framework is proposed, within which a Bayesian recurrent neural network-based probabilistic wind prediction module is integrated into the control design process, yielding a stochastic optimal control problem (OCP) with predefined trajectory violation probabilities. On the other hand, computational cost from solving the complex OCP hinders the real-time implementation of the control strategy on resource-limited flight management systems. To alleviate this burden, state-related inequality constraints are projected from the state space into the input space. Rigorous theoretical guarantees for the proposed Bayesian MPC scheme are provided, including proof of asymptotic stability and derivation of necessary conditions to ensure recursive feasibility. The effectiveness of the proposed method is validated through simulation tests on 4-D flight trajectory tracking problems using reliable datasets.