Federated Behavioral Identification via Grassmann Manifold Aggregation

Abstract

This letter studies the identification of linear systems using behaviors generated by multiple similar systems. Instead of estimating a parametric model, we adopt a framework rooted in behavioral systems theory, where restricted behaviors correspond to fixed-dimensional linear subspaces represented as points on the Grassmann manifold. Motivated by federated learning, we develop a manifold-based aggregation mechanism that combines information from multiple systems while preserving data privacy. The method aggregates locally identified behavior subspaces via geometric operations on the Grassmann manifold, enabling collaborative system identification without sharing raw data. We show that, under mild assumptions, the aggregated identification is stable in the sense that its error is bounded by a constant multiple of the local identification error. Under stronger conditions, we further establish that the identification accuracy improves as the number of participating systems increases. Numerical simulations demonstrate that the proposed approach accurately reconstructs the system dynamics using data from multiple similar systems.