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. Note to Practitioners—Trajectory-based operations in ATM typically require high-precision 4-D trajectory tracking of aircraft. However, conventional MPC struggles to handle precise trajectory tracking tasks under external uncertainties from wind. This work provides new insights into MPC by integrating a Bayesian recurrent neural network that predicts the unknown wind, thereby formulating a Bayesian MPC scheme which can remove the reliance on prior knowledge of the wind. To enhance computational efficiency, a constraint projection technique is employed to address the constrained optimization problem arising from Bayesian MPC. The practicality of this approach is further improved by pre-adjusting the boundaries of the approximated constraints using empirical data. A theoretical analysis is conducted to verify the recursive feasibility of the proposed Bayesian MPC scheme. Simulation tests are performed on Boeing aircraft by using reliable datasets to validate the effectiveness of the proposed method.
