Echo State Networks Simulation of SIR Distributed Control

Echo State Networks (ESNs) have been shown to be effective for a number of tasks, including motor control, dynamic time series prediction, and memorising musical sequences. In this paper, we propose a new task of ESNs in order to solve distributed optimal control problems for systems governed by parabolic differential equations with discrete time delay using an adaptive critic designs. The optimal control problems are discretised by using a finite element method in time and space, then transcribed into a nonlinear programming problems. To find optimal controls and optimal trajectories ESNs adaptive critic designs are used to approximate co-state equations. The efficiency of our approach is demonstrated for a SIR distributed system to control the spread of diseases.