Optimal Centered Active Excitation in Linear System Identification

TL;DR

This paper introduces an active learning algorithm for linear system identification that achieves minimal sample complexity using optimal centered noise excitation, based on least squares and semidefinite programming.

Contribution

It establishes lower bounds for sample complexity and presents an algorithm that matches these bounds, improving efficiency in linear system identification.

Findings

The algorithm attains the minimal sample complexity up to universal factors.

Lower bounds for sample complexity are established for any active learning method.

The bounds explicitly depend on system parameters like state dimension.

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.