Robust control and data reconstruction for nonlinear epidemiological models using feedback linearization and state estimation

Balázs Csutak; Gábor Szederkényi; Balázs Csutak; Gábor Szederkényi

doi:10.3934/mbe.2025006

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 1: 109-137. doi: 10.3934/mbe.2025006

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Research article

Robust control and data reconstruction for nonlinear epidemiological models using feedback linearization and state estimation

Balázs Csutak ¹,
Gábor Szederkényi ^{1,2
,
,}

1.
Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/A, H-1083, Budapest, Hungary
2.
Systems and Control Laboratory, HUN-REN Institute for Computer Science and Control, Kende u. 13-17, H-1111, Budapest, Hungary

Received: 06 August 2024 Revised: 22 September 2024 Accepted: 17 October 2024 Published: 02 January 2025

It has been clearly demonstrated over the past years that control theory can provide an efficient framework for the solution of several complex tasks in epidemiology. In this paper, we present a computational approach for the state estimation based reference tracking control and historical data reconstruction using nonlinear compartmental epidemic models. The control model is given in nonlinear input-affine form, where the manipulable input is the disease transmission rate influenced by possible measures and restrictions, while the observed or computed output is the number of infected people. The control design is built around a simple SEIR model and relies on a feedback linearization technique. We examine and compare different control setups distinguished by the availability of state information, complementing the directly measurable data with an extended Kalman filter used for state estimation. To illustrate the capabilities and robustness of the proposed method, we carry out multiple case studies for output tracking and data reconstruction on Swedish and Hungarian data, all in the presence of serious model and parameter mismatch. Computation results show that a well-designed feedback, even in the presence of significant observation uncertainties, can sufficiently reduce the effect of modeling errors.
- epidemic models,
- compartmental models,
- nonlinear control,
- feedback linearization,
- state estimation,
- data reconstruction
Citation: Balázs Csutak, Gábor Szederkényi. Robust control and data reconstruction for nonlinear epidemiological models using feedback linearization and state estimation[J]. Mathematical Biosciences and Engineering, 2025, 22(1): 109-137. doi: 10.3934/mbe.2025006

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Abstract

It has been clearly demonstrated over the past years that control theory can provide an efficient framework for the solution of several complex tasks in epidemiology. In this paper, we present a computational approach for the state estimation based reference tracking control and historical data reconstruction using nonlinear compartmental epidemic models. The control model is given in nonlinear input-affine form, where the manipulable input is the disease transmission rate influenced by possible measures and restrictions, while the observed or computed output is the number of infected people. The control design is built around a simple SEIR model and relies on a feedback linearization technique. We examine and compare different control setups distinguished by the availability of state information, complementing the directly measurable data with an extended Kalman filter used for state estimation. To illustrate the capabilities and robustness of the proposed method, we carry out multiple case studies for output tracking and data reconstruction on Swedish and Hungarian data, all in the presence of serious model and parameter mismatch. Computation results show that a well-designed feedback, even in the presence of significant observation uncertainties, can sufficiently reduce the effect of modeling errors.

References

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