Joint learning of linear time-invariant dynamical systems (Q6550232)

The problem of jointly learning multiple linear time-invariant dynamical systems is considered under the assumption that the transition unknown matrices can be expressed using an unknown shared basis matrices. The main result here are the finite-time estimation error bounds. Influence of dimension, spectral radius, eigenvalues multiplicity, tail properties of the noise processes, and heterogeneity among the systems on the estimation accuracy is studied. The illustrative example is included to compare the estimation errors of proposed approach with the conventional least-squares estimates of the transition matrices for each system individually.