Summary of Learning to Stabilize Unknown Lti Systems on a Single Trajectory Under Stochastic Noise, by Ziyi Zhang et al.
Learning to Stabilize Unknown LTI Systems on a Single Trajectory under Stochastic Noise
by Ziyi Zhang, Yorie Nakahira, Guannan Qu
First submitted to arxiv on: 31 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Systems and Control (eess.SY)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper tackles the issue of learning to stabilize unknown noisy Linear Time-Invariant (LTI) systems on a single trajectory. The learn-to-stabilize problem typically suffers from exponential blow-up, where the state norm grows exponentially with the state space dimension. To address this challenge, the authors develop a novel algorithm that decouples the unstable subspace from the stable subspace and only stabilizes the former. The algorithm uses a new analytical framework based on singular-value-decomposition (SVD) to prove that the system is stabilized before the state norm reaches an exponential bound in terms of klogn, where k is the dimension of the unstable subspace. This approach avoids exponential blow-up in dimension for stabilizing LTI systems with noise. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us figure out how to make complex systems stable and predictable when we don’t know much about them beforehand. Right now, this process can get really messy and grow exponentially as the system gets bigger. The researchers came up with a new way to approach this problem by breaking it down into smaller parts and focusing on the most unstable parts of the system. This new method helps prevent the system from getting too crazy and allows us to stabilize it more easily. |
