Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis
This addresses system identification challenges for control theory applications, but appears incremental as it builds on existing regularization and convex optimization techniques.
The paper tackles the problem of identifying low-order systems in the frequency domain by formulating it as an optimization problem with nuclear norm regularization, and derives an upper bound on the sample complexity while validating it through numerical simulations.
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.