Neural Network Modeling of Nonlinear Dynamical Systems

In this work we examine the problem of best approximation of a nonlinear dynamic system by a nonlinear model. Our approach is based on a nonlinear operator inner product and corresponding norm we constructed elsewhere in these proceedings. We use these notions to provide a solution to the nonlinear modeling problem through standard inner-product space theory. Recently popular nonlinear approximation tools, such as neural networks, multivariate adaptive regression splines (MARS), and wavelets, are encompassed by the developed theory. New approximation methodologies are suggested as a result of our approach.