Hessians in Birkhoff-Theoretic Trajectory Optimization
arXiv:2511.13963 · doi:10.2514/1.G008778
Abstract
This paper derives various Hessians associated with Birkhoff-theoretic methods for trajectory optimization. According to a theorem proved in this paper, approximately 80% of the eigenvalues are contained in the narrow interval [-2, 4] for all Birkhoff-discretized optimal control problems. A preliminary analysis of computational complexity is also presented with further discussions on the grand challenge of solving a million point trajectory optimization problem.
This paper appeared as an Engineering Note in the J. Guid. Control & Dynamics