2025/09/02 by Aurya Javeed, Drew Kouri, Javeed, A. +7
Engineering · Mathematics · #Spacecraft Dynamics and Control #Numerical methods for differential equations #Advanced Optimization Algorithms Research
paper · pdf · doi:10.48550/arxiv.2509.01855
One might argue that solving a trajectory optimization problem over a million grid points is preposterous. How about solving such a problem at an incredibly fast computational time? On a small form-factor processor? Algorithmic details that make possible this trifecta of breakthroughs are presented in this paper. The computational mathematics that deliver these advancements are: (i) a Birkhoff-theoretic discretization of optimal control problems, (ii) matrix-free linear algebra leveraging Krylov-subspace methods, and (iii) a near-perfect Birkhoff preconditioner that helps achieve O(1) iteration speed with respect to the grid size,~N. A key enabler of this high performance is the computation of Birkhoff matrix-vector products at O(Nlog(N)) time using fast Fourier transform techniques that eliminate traditional computational bottlenecks. A numerical demonstration of this unprecedented scale and speed is illustrated for a practical astrodynamics problem.