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

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.