Abstract
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable finite Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control problem into an unconstrained optimization one is proposed. A quadratic control problem in the context of Newtonian mechanics is solved to demonstrate the proposed algorithm and 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, suggesting a general bound for problems with state space of n dimensions.
Recommended Citation
G. Nicolosi et al., "Approximations and Bounds for Optimal Controls via Finite Fourier Series," Physica Scripta, vol. 100, no. 4, article no. 045201, IOP Publishing; Royal Swedish Academy of Sciences, Apr 2025.
The definitive version is available at https://doi.org/10.1088/1402-4896/adb7a2
Department(s)
Engineering Management and Systems Engineering
Publication Status
Open Access
Keywords and Phrases
approximation; automatic differentiation; optimal control of physical models; pseudospectral methods
International Standard Serial Number (ISSN)
1402-4896; 0031-8949
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 IOP Publishing; Royal Swedish Academy of Sciences, All rights reserved.
Publication Date
01 Apr 2025
Comments
National Science Foundation, Grant CMMI-1932991