Near optimal finite time identification of arbitrary linear dynamical systems

摘要: We derive finite time error bounds for estimating general linear time-invariant (LTI) systems from a single observed trajectory using the method of least squares. provide first analysis case when eigenvalues LTI system are arbitrarily distributed in three regimes: stable, marginally and explosive. Our yields sharp upper each these cases separately. observe that although underlying process behaves quite differently regimes, systematic self--normalized martingale difference term helps bound identification up to logarithmic factors lower bound. On other hand, we demonstrate squares solution may be statistically inconsistent under certain conditions even signal-to-noise ratio is high.