COMPLETE MEMORY STRUCTURES FOR APPROXIMATING NONLINEAR DISCRETE-TIME MAPPINGS

This paper introduces a general structure that is capable of approxima ting input-output maps of nonlinear discrete-time systems, The structu re is comprised of two stages, a dynamical stage followed by a memoryl ess nonlinear stage, A theorem is presented which gives a simple neces sary and sufficient condition for a large set of structures of this fo rm to be capable of modeling a wide class of nonlinear discrete-time s ystems, In particular, we introduce the concept of a ''complete memory .'' A structure with a complete memory dynamical stage and a sufficien tly powerful memoryless stage is shown to be capable of approximating arbitrarily well a wide class of continuous, causal, time-invariant, a pproximately-finite-memory mappings between discrete-time signal space s, Furthermore we show that any bounded-input bounded-output, time-inv ariant, causal memory structure has such an approximation capability i f and only if it is a complete memory, Several examples of linear and nonlinear complete memories are presented, The proposed complete memor y structure provides a template for designing a wide variety of artifi cial neural networks for nonlinear spatiotemporal processing.