A Multidimensional Fourier Approximation of Optimal Control Surfaces
Abstract
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control problem into an unconstrained optimization one is proposed and two problems are solved: a quadratic control problem in the context of Newtonian mechanics, and a control problem arising from an odd-circulant game ruled by the replicator dynamics. Various computational results are presented. Use of automatic differentiation is explored to circumvent the elaborated gradient computation in the first-order optimization procedure. Furthermore, mean square error bounds are derived for the case of one and two-dimensional Fourier series approximations, inducing a general bound for problems of dimensions.
Cite
@article{arxiv.2306.16569,
title = {A Multidimensional Fourier Approximation of Optimal Control Surfaces},
author = {Gabriel Nicolosi and Terry Friesz and Christopher Griffin},
journal= {arXiv preprint arXiv:2306.16569},
year = {2023}
}