Optimal Centered Active Excitation in Linear System Identification

Abstract:We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity while allowing for efficient computation of an estimate of a system matrix. More specifically, we first establish lower bounds of the sample complexity for any active learning algorithm to attain the prescribed accuracy and confidence levels. Next, we derive a sample complexity upper bound of the proposed algorithm, which matches the lower bound for any algorithm up to universal factors. Our tight bounds are easy to interpret and explicitly show their dependence on the system parameters such as the state dimension.

Optimization and Control (math.OC); Machine Learning (cs.LG); Systems and Control (eess.SY); Machine Learning (stat.ML)

arXiv:2604.05518 [math.OC]

(or arXiv:2604.05518v2 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2604.05518 Focus to learn more arXiv-issued DOI via DataCite

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