Summary of Learning Unstable Continuous-time Stochastic Linear Control Systems, by Reza Sadeghi Hafshejani et al.
Learning Unstable Continuous-Time Stochastic Linear Control Systems
by Reza Sadeghi Hafshejani, Mohamad Kazem Shirani Fradonbeh
First submitted to arxiv on: 17 Sep 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed method aims to identify stochastic continuous-time dynamics using a single finite-length state trajectory. A randomized control input approach is employed to estimate the possibly unstable open-loop matrix. Theoretical performance guarantees are established, demonstrating that estimation error decays with trajectory length, excitability, and signal-to-noise ratio, while growing with dimension. Numerical illustrations will be provided to showcase learning rates of dynamics. Additionally, new technical tools are developed for non-asymptotic stochastic bounds on highly non-stationary martingales and generalized laws of iterated logarithms. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper explores a way to identify complex dynamic systems from just one example of how the system behaves over time. The method uses special types of random inputs to estimate the underlying dynamics, even if they’re unstable or hard to predict. The authors show that their approach can accurately model these systems as more data is collected, and provide examples to illustrate how well it works. |
