Optimal Centered Active Excitation in Linear System Identification

2026-04-07

AI Summary

This study addresses the problem of efficiently identifying the system matrix of a linear dynamical system with minimal samples while guaranteeing estimation accuracy and confidence. To this end, the authors propose an active learning algorithm based on optimal centered-noise excitation, which integrates ordinary least squares, semidefinite programming, and optimal experimental design. The method establishes, for the first time, tight upper and lower bounds on sample complexity under active learning, achieving theoretically optimal sample efficiency that matches the information-theoretic lower bound. Furthermore, the approach exhibits strong computational scalability and explicitly characterizes the dependence of sample complexity on key parameters such as the state dimension of the system.

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.

Problem

• linear system identification
• active excitation
• sample complexity
• centered noise
• system matrix estimation

Innovation

• active learning
• linear system identification
• optimal excitation
• sample complexity
• semidefinite programming