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arXiv · 2306.16569

A Multidimensional Fourier Approximation of Optimal Control Surfaces

Gabriel Nicolosi·Terry Friesz·Christopher Griffin
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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 $n$ dimensions.

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Gabriel Nicolosi, Terry Friesz, Christopher Griffin. 2023-06-28. A Multidimensional Fourier Approximation of Optimal Control Surfaces. https://arxiv.org/abs/2306.16569

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