Computation of boundary control of controlled heat equation using artificial neural networks

A method of computing boundary control of semilinear controlled heat equation is proposed. Artificial Neural Network (ANN) based controller has been designed. Control terms are approximated by neural networks and a trial solution is written for the controlled heat equation as a sum of two terms. The first term satisfies the given initial, boundary and final conditions and the second term is a feed-forward neural network, constructed so as not to affect the given conditions. Then the networks are trained to satisfy the heat equation and associated initial, boundary and final conditions.