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arXiv · 2311.11151

On the Hardness of Learning to Stabilize Linear Systems

Xiong Zeng·Zexiang Liu·Zhe Du·Necmiye Ozay·Mario Sznaier
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Abstract

Inspired by the work of Tsiamis et al. \cite{tsiamis2022learning}, in this paper we study the statistical hardness of learning to stabilize linear time-invariant systems. Hardness is measured by the number of samples required to achieve a learning task with a given probability. The work in \cite{tsiamis2022learning} shows that there exist system classes that are hard to learn to stabilize with the core reason being the hardness of identification. Here we present a class of systems that can be easy to identify, thanks to a non-degenerate noise process that excites all modes, but the sample complexity of stabilization still increases exponentially with the system dimension. We tie this result to the hardness of co-stabilizability for this class of systems using ideas from robust control.

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Xiong Zeng, Zexiang Liu, Zhe Du, Necmiye Ozay, Mario Sznaier. 2023-11-18. On the Hardness of Learning to Stabilize Linear Systems. https://arxiv.org/abs/2311.11151

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