Inversion of multilayer neural network with modelling error compensation

Abstract

The main contribution of this paper is to develop a method, using the Newton-Raphson method, to search for the unknown part of the inputs of a multilayer neural network with given outputs and known inputs. To use the Newton-Raphson method, a method of expressing a jacobian by neural network parameters is developed first. A locally linearized relation between inputs and outputs of neural network is then derived. With this, iterative Newton-Raphson searches are performed until satisfactory results are obtained. The method shows rapid convergence, compared with previous approaches. While deriving the inverse of the neural network, some types of optimality, which are problem dependent, are resolved. Although the method shows fast convergence, this type of solution yields some inversion error due to the neural network modelling error. The second contribution of this paper is to propose a novel structure which can eliminate the inversion error caused by the neural network modelling error. The proposed method has a simple structure, but shows good performance as it has a feedforward structure and other beneficial features. Through computer experiments, the proposed methods show good performances in solving inverse kinematics of redundant robots and controlling nonlinear plant.