Sample Complexity Bounds for Linear System Identification from a Finite Set
This work addresses system identification for control or signal processing applications, offering theoretical guarantees that are incremental improvements over existing bounds.
The paper tackles the problem of identifying a linear time-invariant system from a finite set using trajectory data, providing upper and lower bounds on the sample complexity for maximum likelihood estimation without requiring stability assumptions.
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.