# Learning Sparse Dynamical Systems from a Single Sample Trajectory

arXiv: https://arxiv.org/abs/1904.09396 · HTML: https://mlsanity.com/paper/1904.09396/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2019.

## Built on by (most cited first, 20 of 20)

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- [Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputs](https://mlsanity.com/paper/2110.00852/) (2021)
- [Outlier-Robust Linear System Identification Under Heavy-tailed Noise](https://mlsanity.com/paper/2501.00421/) (2024)
- [Learning the Dynamics of Sparsely Observed Interacting Systems](https://mlsanity.com/paper/2301.11647/) (2023)
- [Exact Recovery for System Identification with More Corrupt Data than Clean Data](https://mlsanity.com/paper/2305.10506/) (2023)
- [Learning Decentralized Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2210.08886/) (2022)
- [Online Optimization and Ambiguity-based Learning of Distributionally Uncertain Dynamic Systems](https://mlsanity.com/paper/2102.09111/) (2021)
- [Worst-Case Distance-Aware Error Bounds for Neural Networks](https://mlsanity.com/paper/2510.22021/) (2025)
- [Symmetric Linear Dynamical Systems are Learnable from Few Observations](https://mlsanity.com/paper/2512.05337/) (2025)

## Abstract (arXiv)

This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into account their sparse nature. Assuming that the system is stable, or that it is equipped with an initial stabilizing controller, we provide sharp finite-time guarantees on the accurate recovery of both the sparsity structure and the parameter values of the system. In particular, we show that the proposed estimator can correctly identify the sparsity pattern of the system matrices with high probability, provided that the length of the sample trajectory exceeds a threshold. Furthermore, we show that this threshold scales polynomially in the number of nonzero elements in the system matrices, but logarithmically in the system dimensions --- this improves on existing sample complexity bounds for the sparse system identification problem. We further extend these results to obtain sharp bounds on the ℓ∞-norm of the estimation error and show how different properties of the system---such as its stability level and textitmutual incoherency---affect this bound. Finally, an extensive case study on power systems is presented to illustrate the performance of the proposed estimation method.