# A State Alignment-Centric Approach to Federated System Identification: The FedAlign Framework

arXiv: https://arxiv.org/abs/2503.12137 · HTML: https://mlsanity.com/paper/2503.12137/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 15 Mar 2025.

## Builds on (most cited first, 11 of 11)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [LDP-Fed: Federated Learning with Local Differential Privacy](https://mlsanity.com/paper/2006.03637/) (2020)
- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Multi-Task Imitation Learning for Linear Dynamical Systems](https://mlsanity.com/paper/2212.00186/) (2022)
- [FedSysID: A Federated Approach to Sample-Efficient System Identification](https://mlsanity.com/paper/2211.14393/) (2022)
- [Identifying the Dynamics of a System by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2204.05446/) (2022)
- [Learning Personalized Models with Clustered System Identification](https://mlsanity.com/paper/2304.01395/) (2023)

## Abstract (arXiv)

This paper presents FedAlign, a Federated Learning (FL) framework particularly designed for System Identification (SYSID) tasks by aligning state representations. Local workers can learn State-Space Models (SSMs) with equivalent representations but different dynamics. We demonstrate that directly aggregating these local SSMs via FedAvg results in a global model with altered system dynamics. FedAlign overcomes this problem by employing similarity transformation matrices to align state representations of local SSMs, thereby establishing a common parameter basin that retains the dynamics of local SSMs. FedAlign computes similarity transformation matrices via two distinct approaches: FedAlign-A and FedAlign-O. In FedAlign-A, we represent the global SSM in controllable canonical form (CCF). We apply control theory to analytically derive similarity transformation matrices that convert each local SSM into this form. Yet, establishing global SSM in CCF brings additional alignment challenges in multi input - multi output SYSID as CCF representation is not unique, unlike in single input - single output SYSID. In FedAlign-O, we address these alignment challenges by reformulating the local parameter basin alignment problem as an optimization task. We determine the parameter basin of a local worker as the common parameter basin and solve least square problems to obtain similarity transformation matrices needed to align the remaining local SSMs. Through the experiments conducted on synthetic and real-world datasets, we show that FedAlign outperforms FedAvg, converges faster, and provides improved stability of the global SSM thanks to the efficient alignment of local parameter basins.