# Identifying the Dynamics of a System by Leveraging Data from Similar Systems

arXiv: https://arxiv.org/abs/2204.05446 · HTML: https://mlsanity.com/paper/2204.05446/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 11 Apr 2022.

## Builds on (most cited first, 10 of 10)

- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectories](https://mlsanity.com/paper/2009.00739/) (2020)
- [Predicting with Proxies: Transfer Learning in High Dimension](https://mlsanity.com/paper/1812.11097/) (2018)
- [Nonparametric Finite Time LTI System Identification](https://mlsanity.com/paper/1902.01848/) (2019)
- [Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectories](https://mlsanity.com/paper/2203.12794/) (2022)

## Built on by (most cited first, 15 of 15)

- [FedSysID: A Federated Approach to Sample-Efficient System Identification](https://mlsanity.com/paper/2211.14393/) (2022)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Learning Personalized Models with Clustered System Identification](https://mlsanity.com/paper/2304.01395/) (2023)
- [Learning Dynamical Systems by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2302.04344/) (2023)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Optimizing Closed-Loop Performance with Data from Similar Systems: A Bayesian Meta-Learning Approach](https://mlsanity.com/paper/2211.00077/) (2022)
- [MPC of Uncertain Nonlinear Systems with Meta-Learning for Fast Adaptation of Neural Predictive Models](https://mlsanity.com/paper/2404.12097/) (2024)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [Redefining Clustered Federated Learning for System Identification: The Path of ClusterCraft](https://mlsanity.com/paper/2505.16857/) (2025)
- [Learning Decentralized Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2210.08886/) (2022)
- [Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guarantees](https://mlsanity.com/paper/2311.18769/) (2023)
- [Federated Nonlinear System Identification](https://mlsanity.com/paper/2508.15025/) (2025)
- [Adversarially Robust Multitask Adaptive Control](https://mlsanity.com/paper/2511.05444/) (2025)
- [Joint Learning of Linear Dynamical Systems under Smoothness Constraints](https://mlsanity.com/paper/2406.01094/) (2024)
- [A State Alignment-Centric Approach to Federated System Identification: The FedAlign Framework](https://mlsanity.com/paper/2503.12137/) (2025)

## Abstract (arXiv)

We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and provide finite sample performance guarantees on the quality of the identified dynamics. Our results show that one can effectively use the auxiliary data generated by the similar system to reduce the estimation error due to the process noise, at the cost of adding a portion of error that is due to intrinsic differences in the models of the true and auxiliary systems. We also provide numerical experiments to validate our theoretical results. Our analysis can be applied to a variety of important settings. For example, if the system dynamics change at some point in time (e.g., due to a fault), how should one leverage data from the prior system in order to learn the dynamics of the new system? As another example, if there is abundant data available from a simulated (but imperfect) model of the true system, how should one weight that data compared to the real data from the system? Our analysis provides insights into the answers to these questions.