Nonlinear model predictive control with logic constraints for COVID-19 management
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FEATURE ARTICLE
Nonlinear model predictive control with logic constraints for COVID-19 management Tamás Péni · Balázs Csutak · Gábor Szederkényi · Gergely Röst
Received: 3 August 2020 / Accepted: 23 September 2020 © The Author(s) 2020
Abstract The management of COVID-19 appears to be a long-term challenge, even in countries that have managed to suppress the epidemic after their initial outbreak. In this paper, we propose a model predictive approach for the constrained control of a nonlinear compartmental model that captures the key dynamical properties of COVID-19. The control design uses the discrete-time version of the epidemic model, and it is able to handle complex, possibly time-dependent constraints, logical relations between model variables and multiple predefined discrete levels of interventions. A state observer is also constructed for the computation of non-measured variables from the number of hospital-
ized patients. Five control scenarios with different cost functions and constraints are studied through numerical simulations, including an output feedback configuration with uncertain parameters. It is visible from the results that, depending on the cost function associated with different policy aims, the obtained controls correspond to mitigation and suppression strategies, and the constructed control inputs are similar to real-life government responses. The results also clearly show the key importance of early intervention, the continuous tracking of the susceptible population and that of future work in determining the true costs of restrictive control measures and their quantitative effects.
T. Péni · B. Csutak · G. Szederkényi Institute for Computer Science and Control (SZTAKI), Kende u. 13-17, Budapest 1111, Hungary e-mail: [email protected]
Keywords COVID-19 · Epidemic model · Disease control · Differential equations · Control theory · Model predictive control · Temporal logic
T. Péni Department of Control for Transportation and Vehicle Systems, Faculty of Transportation Engineering and Vehicle Engineering, Budapest University of Technology and Economics, Stoczek u. 2, Budapest 1111, Hungary
1 Introduction
B. Csutak · G. Szederkényi Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/a, Budapest 1083, Hungary e-mail: [email protected] G. Szederkényi e-mail: [email protected] G. Röst (B) Bolyai Institute, University of Szeged, Szeged 6720, Hungary e-mail: [email protected]
On December 31, 2019, China alerted the World Health Organization (WHO) on a cluster of pneumonia cases of unknown origin in Wuhan, China. On January 7, 2020, the causative pathogen of the outbreak was identified as a novel coronavirus, later named as SARSCoV-2, and the disease it causes as COVID-19. SARSCoV-2 infections quickly spread: the first case outside China was identified in Thailand, on 14 January, followed by reported cases from a number of countries [6,56].
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In Europe, the first cases were confirmed on January 24, 2020, in Fr
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