Linear System Identification Under Multiplicative Noise from Multiple Trajectory Data

TL;DR

This paper introduces a method for identifying linear systems affected by multiplicative noise using multiple trajectory data, employing exploratory inputs and least-squares estimation to determine system parameters and noise covariances.

Contribution

It presents a novel approach combining exploratory inputs with least-squares estimation for simultaneous identification of system parameters and noise covariances in multiplicative noise models.

Findings

Proposes a least-squares algorithm for parameter and covariance estimation.

Proves identifiability of covariance structure and estimator consistency.

Demonstrates effectiveness through numerical simulations.

Abstract

The study of multiplicative noise models has a long history in control theory but is re-emerging in the context of complex networked systems and systems with learning-based control. We consider linear system identification with multiplicative noise from multiple state-input trajectory data. We propose exploratory input signals along with a least-squares algorithm to simultaneously estimate nominal system parameters and multiplicative noise covariance matrices. Identifiability of the covariance structure and asymptotic consistency of the least-squares estimator are demonstrated by analyzing first and second moment dynamics of the system. The results are illustrated by numerical simulations.