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

arXiv: https://arxiv.org/abs/2111.04704 · HTML: https://mlsanity.com/paper/2111.04704/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 41 references that are in the map.
- First posted on arXiv 8 Nov 2021.

## Builds on (most cited first, 14 of 14)

- [Distributionally Robust Chance Constrained Data-enabled Predictive Control](https://mlsanity.com/paper/2006.01702/) (2020)
- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [Data-Driven Reachability Analysis with Christoffel Functions](https://mlsanity.com/paper/2104.13902/) (2021)
- [Data-Driven Reachability Analysis Using Matrix Zonotopes](https://mlsanity.com/paper/2011.08472/) (2020)
- [Learning Density Distribution of Reachable States for Autonomous Systems](https://mlsanity.com/paper/2109.06728/) (2021)
- [On-The-Fly Control of Unknown Smooth Systems from Limited Data](https://mlsanity.com/paper/2009.12733/) (2020)
- [Data-Driven Set-Based Estimation using Matrix Zonotopes with Set Containment Guarantees](https://mlsanity.com/paper/2101.10784/) (2021)
- [State-Based Confidence Bounds for Data-Driven Stochastic Reachability Using Hilbert Space Embeddings](https://mlsanity.com/paper/2010.08036/) (2020)
- [Reachability of Black-Box Nonlinear Systems after Koopman Operator Linearization](https://mlsanity.com/paper/2105.00886/) (2021)
- [Robust Data-Enabled Predictive Control: Tractable Formulations and Performance Guarantees](https://mlsanity.com/paper/2105.07199/) (2021)
- [Robust Data-Driven Predictive Control using Reachability Analysis](https://mlsanity.com/paper/2103.14110/) (2021)
- [Data-Driven Approach for Uncertainty Propagation and Reachability Analysis in Dynamical Systems](https://mlsanity.com/paper/2001.07668/) (2020)
- [Dissipativity verification with guarantees for polynomial systems from noisy input-state data](https://mlsanity.com/paper/2008.03231/) (2020)
- [Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems](https://mlsanity.com/paper/1908.09950/) (2019)

## Abstract (arXiv)

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.