Adaptive signal processing
System identification: theory for the user
System identification: theory for the user
Adaptive filter theory (3rd ed.)
Adaptive filter theory (3rd ed.)
Neural network approach to optimal filtering
WCNA '92 Proceedings of the first world congress on World congress of nonlinear analysts '92, volume IV
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Neural and Adaptive Systems: Fundamentals through Simulations with CD-ROM
Neural and Adaptive Systems: Fundamentals through Simulations with CD-ROM
IEEE Transactions on Neural Networks
Adaptive multilayer perceptrons with long- and short-term memories
IEEE Transactions on Neural Networks
Training Recurrent Neurocontrollers for Robustness With Derivative-Free Kalman Filter
IEEE Transactions on Neural Networks
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By a fundamental neural filtering theorem, a recurrent neural network with fixed weights is known to be capable of adapting to an uncertain environment. This letter reports some mathematical results on the performance of such adaptation for series-parallel identification of a dynamical system as compared with the performance of the best series-parallel identifier possible under the assumption that the precise value of the uncertain environmental process is given. In short, if an uncertain environmental process is observable (not necessarily constant) from the output of a dynamical system or constant (not necessarily observable), then a recurrent neural network exists as a series-parallel identifier of the dynamical system whose output approaches the output of an optimal series-parallel identifier using the environmental process as an additional input.