# Learning for Optimization & Control IV – Invited Special Session

## A5L-F: Learning for Optimization & Control IV - Invited Special Session

Session Type: Lecture
Session Code: A5L-F
Location: Room 6
Date & Time: Wednesday March 22, 2023 (15:20-16:20)
3169On the Sample Complexity of Stabilizing LTI Systems on a Single TrajectoryYang Hu{3}, Adam Wierman{1}, Guannan Qu{2}Stabilizing an unknown dynamical system is one of the central problems in control theory. In this paper, we study the sample complexity of the learn-to-stabilize problem in Linear Time-Invariant (LTI) systems on a single trajectory. Current state-of-the-art approaches require a sample complexity linear in $n$, the state dimension, which incurs a state norm that blows up exponentially in $n$. We propose a novel algorithm based on spectral decomposition that only needs to learn a small part of the dynamical matrix acting on its unstable subspace. We show that, under proper assumptions, our algorithm stabilizes an LTI system on a single trajectory with $\\tilde{O}(k)$ samples, where $k$ is the instability index of the system. This represents the first sub-linear sample complexity result for the stabilization of LTI systems under the regime when $k=o(n)$