Structure theorems for nonlinear systems
Multidimensional Systems and Signal Processing
Approximation and radial-basis-function networks
Neural Computation
Approximation by superposition of sigmoidal and radial basis functions
Advances in Applied Mathematics
Fading-memory feedback systems and robust stability
Automatica (Journal of IFAC) - Special issue on robust control
Approximation of Myopic Systems Whose Inputs Need Not BeContinuous
Multidimensional Systems and Signal Processing
Complete memory structures for approximating nonlinear discrete-time mappings
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
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Thispaper considerably extends recent discrete-time (and discrete-space)results concerning the problem of obtaining criteria under whichinput-output maps can be uniformly approximated arbitrarily wellusing a certain structure consisting of a not-necessarily lineardynamic part followed by a nonlinear memoryless section thatmay contain sigmoids or radial basis functions, etc. In thoseresults certain separation conditions of the kind associatedwith the Stone-Weierstrass theorem play a prominent role andemerge as criteria for approximation—not just sufficientconditions under which an approximation exists. Here we givecorresponding results for a much larger set of maps of interest.More specifically, corresponding results are given for an importantfamily of continuous-time and continuous space systems. As anexample, it is shown that a large class of continuous-space myopicsystems with continuous inputs can be uniformly approximatedarbitrarily well using just a bank of shift operators followedby a nonlinear memoryless section. This directs attention toapproximants for such systems of a very different type than thosediscussed earlier in the literature. In another example, a newresult is given concerning the uniform approximation of a largeclass of myopic continuous-time systems with inputs that mayhave discontinuities.