  We study the problem of learning a linear system model from the observations
of $M$ clients. The catch: Each client is observing data from a different
dynamical system. This work addresses the question of how multiple clients
collaboratively learn dynamical models in the presence of heterogeneity. We
pose this problem as a federated learning problem and characterize the tension
between achievable performance and system heterogeneity. Furthermore, our
federated sample complexity result provides a constant factor improvement over
the single agent setting. Finally, we describe a meta federated learning
algorithm, FedSysID, that leverages existing federated algorithms at the client
level.
