Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis

TL;DR

This paper introduces a frequency-domain system identification method for low-order systems, utilizing nuclear norm regularization and providing finite-sample complexity bounds with validation through simulations.

Contribution

It presents a convex optimization-based approach with theoretical bounds on sample complexity and error, specifically tailored for low-order system identification.

Findings

Derived an upper bound on sampled-frequency complexity

Extended bounds to characterize identification error across all frequencies

Validated the method's effectiveness through numerical simulations

Abstract

This paper proposes a frequency-domain system identification method for learning low-order systems. The identification problem is formulated as the minimization of the l2 norm between the identified and measured frequency responses, with the nuclear norm of the Loewner matrix serving as a regularization term. This formulation results in an optimization problem that can be efficiently solved using standard convex optimization techniques. We derive an upper bound on the sampled-frequency complexity of the identification process and subsequently extend this bound to characterize the identification error over all frequencies. A detailed analysis of the sample complexity is provided, along with a thorough interpretation of its terms and dependencies. Finally, the efficacy of the proposed method is demonstrated through an example, and numerical simulations validating the growth rate of the sample complexity bound.