2024/05/31 by Ziyi Zhang, Zhang, Ziyi, Yorie Nakahira +3
Computer Science · Engineering · #Control Systems and Identification #FOS: Computer and information sciences #FOS: Electrical engineering #Fault Detection and Control Systems #Machine Learning (cs.LG) #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2406.00234
openalex publication_date 2024/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of learning to stabilize unknown noisy Linear Time-Invariant (LTI) systems on a single trajectory. It is well known in the literature that the learn-to-stabilize problem suffers from exponential blow-up in which the state norm blows up in the order of Θ(2n) where n is the state space dimension. This blow-up is due to the open-loop instability when exploring the n-dimensional state space. To address this issue, we develop a novel algorithm that decouples the unstable subspace of the LTI system from the stable subspace, based on which the algorithm only explores and stabilizes the unstable subspace, the dimension of which can be much smaller than n. With a new singular-value-decomposition(SVD)-based analytical framework, we prove that the system is stabilized before the state norm reaches 2O(k log n), where k is the dimension of the unstable subspace. Critically, this bound avoids exponential blow-up in state dimension in the order of Θ(2n) as in the previous works, and to the best of our knowledge, this is the first paper to avoid exponential blow-up in dimension for stabilizing LTI systems with noise.