Multilayer neural networks for solving a class of partial differential equations

Abstract

In this paper, training the derivative of a feedforward neural network with the extended backpropagation algorithm is presented. The method is used to solve a class of first-order partial differential equations for input-to-state linearizable or approximate linearizable systems. The solution of the differential equation, together with the Lie derivatives, yields a change of coordinates. A feedback control law is then designed to keep the system in a desired behavior. The examination of the proposed method, through simulations, exhibits the advantages of it. They include easily and quickly finding approximate solutions for complicated first-order partial differential equations. Therefore, the work presented here can benefit the design of the class of nonlinear control systems, where the nontrivial solutions of the partial differential equations are difficult to find.