Optimal Control for Minimizing Inescapable Ellipsoids in Linear Periodically Time-Varying Systems Under Bounded Disturbances
Optimization and Control
2025-09-05 v1 Systems and Control
Systems and Control
Abstract
This letter addresses optimal controller design for periodic linear time-varying systems under unknown-but-bounded disturbances. We introduce differential Lyapunov-type equations to describe time-varying inescapable ellipsoids and define an integral-based measure of their size. To minimize this measure, we develop a differential Riccati equation-based approach that provides exact solutions for state-feedback, observer synthesis, and output-feedback control. A key component is a systematic procedure for determining the optimal time-varying parameter, reducing an infinite-dimensional optimization to a simple iterative process. A numerical example validates the method's effectiveness.
Keywords
Cite
@article{arxiv.2509.04090,
title = {Optimal Control for Minimizing Inescapable Ellipsoids in Linear Periodically Time-Varying Systems Under Bounded Disturbances},
author = {Egor Dogadin and Alexey Peregudin},
journal= {arXiv preprint arXiv:2509.04090},
year = {2025}
}