Active Learning for Identification of Linear Dynamical Systems
This work addresses the challenge of efficient system identification for control and modeling applications, offering a novel approach with proven optimality, though it is incremental in the context of active learning methods.
The authors tackled the problem of estimating parameters of linear dynamical systems by proposing an active learning algorithm that adaptively chooses inputs to accelerate estimation, achieving asymptotic optimality with finite time bounds and showing improvement over Gaussian noise excitation.
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.