Learning Fractional-Order Dynamics from a Single Trajectory
Many real-world processes exhibit long-range dependence, where the current state depends on a slowly decaying trace of past states rather than on the most recent state alone. This paper studies system identification for discrete-time fractional-order linear time-invariant systems from a single observed trajectory of length $t$, a setting that captures such non-Markovian dynamics through the Grünwald--Letnikov difference operator. Unlike Markovian systems, fractional-order systems couple estimation across the entire history, making both statistical analysis and practical identification more challenging. We propose \emph{Fractional-Order Ordinary-Least-Squares Grid-Search (FO-GS)}, a simple...
| Authors | Xiaole Zhang, Ziyi Zhang, Zehao Zhao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 September 2026 |
| Last updated at source | 16 September 2026 |
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