Linear System Identification under Multiplicative Noise from Multiple Trajectory Data
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.
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.
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