Online Identification of Time-Varying Systems Using Excitation Sets and Change Point Detection

TL;DR

This paper introduces a novel online identification method for time-varying systems that uses excitation sets and change point detection to improve parameter estimation and adapt to system changes.

Contribution

It proposes the concept of optimal excitation sets, a greedy excitation set-based recursive least squares algorithm, and a memory resetting scheme for better tracking of time-varying parameters.

Findings

The proposed method effectively tracks time-varying parameters in networked epidemic models.

It outperforms conventional approaches in numerical case studies.

The algorithms handle lack of persistent excitation and system changes efficiently.

Abstract

In this work, we first show that the problem of parameter identification is often ill-conditioned and lacks the persistence of excitation required for the convergence of online learning schemes. To tackle these challenges, we introduce the notion of optimal and greedy excitation sets which contain data points with sufficient richness to aid in the identification task. We then present the greedy excitation set-based recursive least squares algorithm to alleviate the problem of the lack of persistent excitation, and prove that the iterates generated by the proposed algorithm minimize an auxiliary weighted least squares cost function. When data points are generated from time-varying parameters, online estimators tend to underfit the true parameter trajectory, and their predictability deteriorates. To tackle this problem, we propose a memory resetting scheme leveraging change point detection techniques. Finally, we illustrate the performance of the proposed algorithms via several numerical case studies to learn the (time-varying) parameters of networked epidemic dynamics, and compare it with results obtained using conventional approaches.