Generalised neurofuzzy network modelling algorithms using Bezier Bernstein polynomial functions and additive decomposition

Abstract

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bezier Bernstein polynomial functions. This paper is generalised in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n.. This new construction algorithm also introduces univariate Bezier Bernstein polynomial functions for the completeness of the generalised procedure. Like the B-spline expansion based neurofuzzy systems, Bezier Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modelling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bezier Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modelling approach.

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