Integrating Optimal Control and Machine Learning for Energy-Efficient UAV Flight

This paper demonstrates the application of an integrated optimal control and machine learning (ML) framework to the problem of fuel-optimal trajectory generation for an ultra-long-endurance, fixed-wing unmanned aerial vehicle (UAV) equipped with a realistic propulsion system: an internal combustion engine and a variable pitch propeller. The objective is to compute minimum-fuel flight trajectories through time-varying, three-dimensional weather fields over multi-day autonomous missions. The trajectory optimization problem is formulated using Pontryagin’s Maximum Principle and is solved numerically as a boundary value problem (BVP). A key challenge lies in incorporating a high-fidelity propulsion model that captures the nonlinear, non-unique mapping between the aircraft state, propulsion controls and performance metrics, while remaining computationally tractable. To address this, a neural network–based digital twin is developed from calibrated ground and flight test data, enabling fast and differentiable approximations of fuel flow rate and propulsion control variables—specifically engine RPM and propeller pitch angle. The digital twin architecture naturally supports the computation of control derivatives required by the BVP solver, significantly improving convergence. The proposed framework unifies high-fidelity physical modeling, machine learning techniques, and optimal control theory to achieve scalable and physically consistent trajectory optimization for a complex and operationally relevant aircraft. Case studies demonstrate fuel-optimal routing through dynamic weather conditions, verifying both the system’s performance and the optimality of the generated trajectories.