Neural Networks Simulation of Distributed SEIR System

• Published in: Mathematics (Basel) Vol. 11; no. 9; p. 2113
• Main Authors: Kmet, Tibor, Kmetova, Maria, Végh, Ladislav
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 29.04.2023
• Subjects: Adaptive control; Algorithms; Approximation; complex systems; Computer networks; Computer simulation; Differential equations; Disease control; distributed control problem with discrete delays; Dynamic programming; Epidemiology; feed-forward neural network; Mathematics; Neural networks; Numerical analysis; Optimal control; optimal control synthesis; Optimization; Parabolic differential equations; Partial differential equations; Simulation methods; state and control constraints; Trajectory control; Trajectory optimization; Variables
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11092113

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.