On determining the structure of a non-linear system

Abstract

A method is presented for constructing a model of a non-linear system from the input-output data. The structure of the system is assembled from a library of nonlinear terms that are possible suspects for inclusion in the model. While each possible model structure is represented by a node in a tree, it is shown that searching the tree for the optimal n-term model structure can be done in n stages using an algorithm based on conjugate direction ideas. The essential feature of the technique is that it generates a sequence of projection matrices such that the original vector-valued functions become conjugate directions. This leaves the original non-linear terms intact and allows the structure for the optimal n-term model to be assembled in n selections from the library. Examples are presented from regression analysis and non-linear dynamic systems.