A neurofuzzy approach to variational problems by using Gaussian membership functions

Abstract

In this paper we propose a neurofuzzy direct solution method for variational problems in which the cost function of an integral form is minimized. We deal with two nonlinear systems; one is a direct drive (DD) manipulator systems, and the other is a trailer-truck system. The DD manipulator system is described by a continuous-time dynamical model, and the trailer-truck system is described by a discrete-time dynamical model. The problem is to find trajectories which minimize the cost function of an integral form. The trajectories of state variables and input variables are represented by fuzzy models that consists of Gaussian membership functions. The networks of Gaussian functions are trained by the steepest-descent method to minimize the cost function. The proposed neurofuzzy approach provides a direct solution method of the variational problems by using Gaussian functions. The function is regarded as a simplifie fuzzy reasoning model and called neurofuzzy.