Sampled-data optimal control of linear fractional-order systems

Pantelis Sopasakis

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arXiv · 2609.12961

Sampled-data optimal control of linear fractional-order systems

Pantelis Sopasakis

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Abstract

This paper studies the problem of optimal control of Caputo linear fractional-order systems of order $α\in (0, 1]$ 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 RIS

Pantelis Sopasakis. 2026-09-11. Sampled-data optimal control of linear fractional-order systems. https://arxiv.org/abs/2609.12961

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