Non-asymptotic Identification of LTI Systems from a Single Trajectory

TL;DR

This paper presents a finite-time method for learning LTI system models from a single trajectory, providing explicit data requirements and stability guarantees for the Ho-Kalman realization process.

Contribution

It introduces a non-asymptotic analysis for system identification from a single trajectory, including stability results for the Ho-Kalman algorithm and sample complexity bounds.

Findings

Finite sample bounds for Markov parameter estimation.

Stability guarantees for the Ho-Kalman realization.

Explicit data requirements for accurate system identification.

Abstract

We consider the problem of learning a realization for a linear time-invariant (LTI) dynamical system from input/output data. Given a single input/output trajectory, we provide finite time analysis for learning the system's Markov parameters, from which a balanced realization is obtained using the classical Ho-Kalman algorithm. By proving a stability result for the Ho-Kalman algorithm and combining it with the sample complexity results for Markov parameters, we show how much data is needed to learn a balanced realization of the system up to a desired accuracy with high probability.