ECS-9703745 Sandberg The general problem of understanding nonlinear mappings from one function space into another is fundamental to a wide range of engineering system studies. The proposed work aims to build a comprehensive understanding of the approximation capabilities, usability and effectiveness of nonlinear networks intended for use in settings involving compensation, adaptivity, identification and signal processing. It is founded on recent results obtained by the proposer showing that very large classes of continuous functionals, shift-invariant maps, and shift-varying maps can be uniformly approximated by certain conceptually simple nonlinear structures. The project will address key issues concerning the advantages, limitations, design and use of such structures. These include the determination of suitable network structures, network size, connectivity patterns and form of nonlinearity for different problem classes, effectiveness of alternate identification algorithms and their convergence rates, and techniques for constructive/destructive network growth. The proposed work will emphasize the development of an analytical basis for design, and will raise the understanding of the capabilities and usability of these nonlinear structures to a level comparable to that achieved at present for (static) multilayered feedforward networks. Important examples of systems to which our results will apply can be drawn from many fields.
