Feasibility of random basis function approximators for modeling and control

Abstract-- We discuss the role of random basis function approximators in modeling and control. We analyze the published work on random basis function approximators and demonstrate that their favorable error rate of convergence O(1/n) is guaranteed only with very substantial computational resources. We also discuss implications of our analysis for applications of neural networks in modeling and control. I. INTRODUCTION Efficient modeling and control of complex systems in the presence of uncertainties is important for modern engineering. This is especially true in the domain of intelligent systems that are designed to operate in uncertain environments. Physical models of such relations f(·) are not always available, and it is quite common to use mathematical substitutes such as, e.g., superpositions of (basis) functions that are capable of approximating a-priori unknown f(·) with the required precision.