Sampled-data optimal control of linear fractional-order systems
Abstract
This paper studies the problem of optimal control of Caputo linear fractional-order systems of order α∈ (0, 1] with continuous-time state constraints and input constraints. The resulting problems are semi-infinite, since the state constraints are imposed over the sampling intervals and not merely at the sampling instants. To address this, we derive a sampled-data representation of the inter-sample trajectory and use Bernstein polynomials to construct polytopic approximations of the continuous-time state constraints. Explicit bounds are obtained for the conservatism introduced by this approximation. By subdividing each sampling interval and applying the Bernstein-based construction on every subinterval, the approximation is made arbitrarily tight. Numerical examples illustrate the tightness of the proposed enclosures, the computational tractability of the proposed method, and the trade-off between approximation accuracy and computational complexity.
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BibTeX
@misc{sopasakis2026sampleddata,
title = {{Sampled-data optimal control of linear fractional-order systems}},
author = {Pantelis Sopasakis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12961},
eprint = {2609.12961},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12961},
}
RIS
TY - UNPB
TI - Sampled-data optimal control of linear fractional-order systems
AU - Pantelis Sopasakis
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12961
UR - https://arxiv.org/abs/2609.12961
AB - This paper studies the problem of optimal control of Caputo linear fractional-order systems of order α∈ (0, 1] with continuous-time state constraints and input constraints. The resulting problems are semi-infinite, since the state constraints are imposed over the sampling intervals and not merely at the sampling instants. To address this, we derive a sampled-data representation of the inter-sample trajectory and use Bernstein polynomials to construct polytopic approximations of the continuous-time state constraints. Explicit bounds are obtained for the conservatism introduced by this approximation. By subdividing each sampling interval and applying the Bernstein-based construction on every subinterval, the approximation is made arbitrarily tight. Numerical examples illustrate the tightness of the proposed enclosures, the computational tractability of the proposed method, and the trade-off between approximation accuracy and computational complexity.
ER -