Active Learning for Identification of Linear Dynamical Systems

TL;DR

This paper introduces an active learning algorithm for efficiently estimating parameters of linear dynamical systems by adaptively selecting inputs, achieving near-optimal estimation rates and outperforming noise-based excitation methods.

Contribution

The paper presents a novel adaptive input selection algorithm with proven finite-time bounds and asymptotic optimality for linear dynamical system identification.

Findings

The algorithm attains near-optimal estimation rates.

Optimal rates are unachievable with Gaussian noise excitation.

Numerical examples demonstrate practical effectiveness.

Abstract

We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound quantifying the estimation rate our algorithm attains and prove matching upper and lower bounds which guarantee its asymptotic optimality, up to constants. In addition, we show that this optimal rate is unattainable when using Gaussian noise to excite the system, even with optimally tuned covariance, and analyze several examples where our algorithm provably improves over rates obtained by playing noise. Our analysis critically relies on a novel result quantifying the error in estimating the parameters of a dynamical system when arbitrary periodic inputs are being played. We conclude with numerical examples that illustrate the effectiveness of our algorithm in practice.