Sample Complexity Bounds for Linear System Identification from a Finite Set

TL;DR

This paper establishes both upper and lower bounds on the number of samples needed to identify a linear time-invariant system from a finite set, without assuming system stability, using information-theoretic and statistical methods.

Contribution

It provides the first finite-sample bounds for LTI system identification that do not depend on stability assumptions, combining maximum likelihood analysis with information theory.

Findings

Upper bound on sample complexity for system identification

Lower bound independent of the estimator used

Analytical and numerical validation of bounds

Abstract

This paper considers a finite sample perspective on the problem of identifying an LTI system from a finite set of possible systems using trajectory data. To this end, we use the maximum likelihood estimator to identify the true system and provide an upper bound for its sample complexity. Crucially, the derived bound does not rely on a potentially restrictive stability assumption. Additionally, we leverage tools from information theory to provide a lower bound to the sample complexity that holds independently of the used estimator. The derived sample complexity bounds are analyzed analytically and numerically.