Data-driven Set-based Estimation of Polynomial Systems with Application to SIR Epidemics

TL;DR

This paper introduces a data-driven set-based estimation method for polynomial nonlinear systems that guarantees real-time state inclusion, demonstrated on an SIR epidemic model, even when system coefficients are unknown.

Contribution

It develops a novel offline-online estimation framework for polynomial systems using input-output data, applicable to real-time state estimation without known polynomial coefficients.

Findings

Successfully applied to SIR epidemic model

Provides guaranteed state inclusion in real-time

Estimates polynomial coefficients from data

Abstract

This paper proposes a data-driven set-based estimation algorithm for a class of nonlinear systems with polynomial nonlinearities. Using the system's input-output data, the proposed method computes a set that guarantees the inclusion of the system's state in real-time. Although the system is assumed to be a polynomial type, the exact polynomial functions, and their coefficients are assumed to be unknown. To this end, the estimator relies on offline and online phases. The offline phase utilizes past input-output data to estimate a set of possible coefficients of the polynomial system. Then, using this estimated set of coefficients and the side information about the system, the online phase provides a set estimate of the state. Finally, the proposed methodology is evaluated through its application on SIR (Susceptible, Infected, Recovered) epidemic model.