Finite-Sample System Identification of Linear Systems Under Random Packet Loss

Abstract

This article investigates finite-sample system identification for discrete-time linear systems subject to random data packet loss. Random data packet loss destroys the usual linear structure of least squares identification, which makes classical nonasymptotic analyses inapplicable. We address this difficulty by viewing the resulting nonlinear least squares estimator as an empirical loss minimizer and developing a statistical learning-based framework to study its performance under packet loss. Under mild assumptions, we derive high-probability finite-sample guarantees for the generalization error that reveal how identification performance improves as more samples are collected, but tends to deteriorate for higher dimensional systems and for longer bursts of packet loss, especially when the underlying dynamics are only weakly stable. By further imposing a local identifiability and strong-convexity condition around the true system matrices, we translate these generalization guarantees into nonasymptotic bounds on the parameter estimation error, which exhibit the same qualitative trends and show that longer packet loss worsen the constants in the bounds, so that more data are required to achieve a given accuracy. The numerical simulation verified the conclusion.