📝 SummarXiv

Abstract

Optimizing commercial aircraft cruise trajectories using the Pontryagin Maximum Principle (PMP) is particularly challenging due to the nonlinear dynamics of aircraft speed, complex costate dynamics, and the inclusion of two continuous controls, one of which (thrust) is typically a singular, affine input. We present a surrogate optimization framework, accounting for space-dependent wind fields, flight-sensitive areas, and equality/inequality constraints. To simulate atmospheric wind, we propose a divergence-free composite inviscid flow model showing structural consistency with large-scale patterns observed in atmospheric wind datasets. Flight-sensitive areas are clustered as parametrized ellipses, considered as soft constraints. Building on turnpike property, the surrogate framework enforces quasi-steady aircraft speed on infinitesimal segments, thereby eliminating the thrust control and treating speed as a direct control. Comprehensive numerical experiments on various setups confirm that the surrogate framework reproduces optimal solutions identical to those of the original problem while significantly reducing computational time and implementation efforts. The accompanying \textbf{supplementary material} includes implementation details and open-source code (with interactive built-in and user-defined environments for aircraft and wind functions, and for flight-sensitive areas), together with an additional example that examines wind-induced variability in optimal solutions via Monte Carlo analysis enabled by the high-speed PMP-based surrogate framework.