Beyond periodicity: Fourier methods for optimal control
Abstract
Fourier-based spectral methods provide compact global approximations, permit simple differentiation and integration, and achieve spectral convergence for smooth periodic functions. Their use in finite-horizon optimal control problems (OCPs) is nevertheless challenged by the generally nonperiodic state and control trajectories: endpoint mismatch induces artificial discontinuities and can destroy spectral convergence. Leveraging Eckhoff-type endpoint-correction techniques, we develop a Fourier-based spectral framework for OCPs with possibly nonlinear dynamics and constraints. The correction improves convergence without enlarging the set of decision variables, yielding an efficient finite-dimensional numerical method. Furthermore, we formulate selected dynamics and obstacle-avoidance constraints through Sobolev residual bounds, which incorporate information about the residuals over the entire time horizon and improve constraint satisfaction. Numerical experiments on benchmark problems demonstrate competitive computational performance, lower residual errors, and improved solution accuracy.
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BibTeX
@misc{ispiryan2026beyond,
title = {{Beyond periodicity: Fourier methods for optimal control}},
author = {Milena Ispiryan and Vahagn Makaryan and Lusine Poghosyan and Tigran Bakaryan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17386},
eprint = {2610.17386},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17386},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Beyond periodicity: Fourier methods for optimal control
AU - Milena Ispiryan
AU - Vahagn Makaryan
AU - Lusine Poghosyan
AU - Tigran Bakaryan
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17386
UR - https://arxiv.org/abs/2610.17386
AB - Fourier-based spectral methods provide compact global approximations, permit simple differentiation and integration, and achieve spectral convergence for smooth periodic functions. Their use in finite-horizon optimal control problems (OCPs) is nevertheless challenged by the generally nonperiodic state and control trajectories: endpoint mismatch induces artificial discontinuities and can destroy spectral convergence. Leveraging Eckhoff-type endpoint-correction techniques, we develop a Fourier-based spectral framework for OCPs with possibly nonlinear dynamics and constraints. The correction improves convergence without enlarging the set of decision variables, yielding an efficient finite-dimensional numerical method. Furthermore, we formulate selected dynamics and obstacle-avoidance constraints through Sobolev residual bounds, which incorporate information about the residuals over the entire time horizon and improve constraint satisfaction. Numerical experiments on benchmark problems demonstrate competitive computational performance, lower residual errors, and improved solution accuracy.
ER -