Orthogonal Least Squares Algorithm for the Approximation of a Map and its Derivatives with a RBF Network

TL;DR

This paper introduces a modified Orthogonal Least Squares algorithm for RBF Networks that can approximate a non-linear map and its derivatives simultaneously, aiding in control and stability analysis.

Contribution

It presents a novel modification to the OLS algorithm enabling RBFNs to estimate derivatives alongside the function, which was not previously possible.

Findings

Effective in approximating both functions and derivatives

Demonstrated on stability analysis of a feedback system

Enhances system identification and control tasks

Abstract

Radial Basis Function Networks (RBFNs) are used primarily to solve curve-fitting problems and for non-linear system modeling. Several algorithms are known for the approximation of a non-linear curve from a sparse data set by means of RBFNs. However, there are no procedures that permit to define constrains on the derivatives of the curve. In this paper, the Orthogonal Least Squares algorithm for the identification of RBFNs is modified to provide the approximation of a non-linear 1-in 1-out map along with its derivatives, given a set of training data. The interest on the derivatives of non-linear functions concerns many identification and control tasks where the study of system stability and robustness is addressed. The effectiveness of the proposed algorithm is demonstrated by a study on the stability of a single loop feedback system.