Linear System Identification Under Multiplicative Noise from Multiple Trajectory Data

Authors: Yu Xing, Benjamin Gravell, Xingkang He, Karl Henrik Johansson, Tyler Summers

Published: 2020 (Conference Paper)

Source: American Control Conference (ACC)

Algorithm: MALS

arXiv: 2002.06613

DOI: 10.23919/ACC45564.2020.9147756

Summary

Provides asymptotic results on convergence of identified system parameters (dynamics parameters and noise covariances) to true values using a trajectory-averaging least-squares estimation algorithm for linear systems with multiplicative noise. Later extended to non-asymptotic results in 2106.16078.

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.

Links

Primary

Paper arxiv.org

Standard

arXiv Abstract 2002.06613 arXiv PDF 2002.06613 arXiv HTML 2002.06613 DOI 10.23919/ACC45564.2020.9147756

Alternate

people.kth.se PDF people.kth.se ieeexplore.ieee.org ieeexplore.ieee.org

Tags

• Linear systems

• System identification

• Trajectory data

• Multiplicative Noise

• Multiple trajectories

• Covariance matrix

• Network system

• Least squares

• Optimal control

• Convergence rate

• Recursive

• Algorithm