  We address the problem of learning linear system models from observing
multiple trajectories from different system dynamics. This framework
encompasses a collaborative scenario where several systems seeking to estimate
their dynamics are partitioned into clusters according to their system
similarity. Thus, the systems within the same cluster can benefit from the
observations made by the others. Considering this framework, we present an
algorithm where each system alternately estimates its cluster identity and
performs an estimation of its dynamics. This is then aggregated to update the
model of each cluster. We show that under mild assumptions, our algorithm
correctly estimates the cluster identities and achieves an approximate sample
complexity that scales inversely with the number of systems in the cluster,
thus facilitating a more efficient and personalized system identification
process.

Optimization and Control;Machine Learning;Systems and Control;Systems and Control