Approximation of a map and its derivatives with an RBF Network using input-output clustering

Radial Basis Function Networks (RBFNs) are widely used in curve-fitting problems and nonlinear dynamical systems modelling. Using the gradient of the function during the training phase leads to a smooth approximation of both the function itself, and its derivatives. The knowledge about gradient of the function in some identification and control tasks is desired, particularly when the stability and robustness of the system are studied. In this paper, a new clustering based algorithm for learning an Input-Output map along with its derivatives using RBFN is proposed. The input-output clustering (IOC) algorithm for the training of an RBFN is modified to improve the performance of the network in approximating a nonlinear single-input single-output map along with its derivatives utilizing a set of input-output data and the first derivative of the function in each data point. The advantage of the proposed algorithm, in comparison with orthogonal least square (OLS), is demonstrated with an example in the field of data interpolation.