Neural Networks Simulation of Distributed SEIR System

Tibor Kmet (), Maria Kmetova and Ladislav Végh
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Tibor Kmet: Department of Informatics, J. Selye University, Bratislavská Cesta 3322, 945 01 Komárno, Slovakia
Maria Kmetova: Department of Mathematics, Faculty of Natural Sciences and Informatics, Constantine the Philosopher University, Tr. A. Hlinku 1, 949 74 Nitra, Slovakia
Ladislav Végh: Department of Informatics, J. Selye University, Bratislavská Cesta 3322, 945 01 Komárno, Slovakia

Mathematics, 2023, vol. 11, issue 9, 1-14

Abstract: In this paper, a neural network-based optimal control synthesis is presented for distributed optimal control problems. We deal with solutions of systems controlled by parabolic differential equations with control and state constraints and discrete time delays. The given optimal control problem is transformed into a discrete nonlinear problem and then implemented into a feed-forward adaptive critic neural network. We propose a new algorithm to reach optimal control and an optimal trajectory using a feed-forward neural network. We present a concrete application of this simulation method on the SEIR (Susceptible—Exposed—Infectious—Recovered) optimal control problem of a distributed system for disease control. The results show that the adaptive-critic-based neural network approach is suitable for the solution of optimal distributed control problems with delay in state and control variables subject to control-state constraints and simulates the spread of disease in the SEIR system.

Keywords: feed-forward neural network; distributed control problem with discrete delays; state and control constraints; optimal control synthesis; complex systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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