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Some Features of Neural Networks as Nonlinearly Parameterized Models of Unknown Systems Using an Online Learning Algorithm

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Document pages: 17 pages

Abstract: This paper deals with deriving the properties ofupdated neural network model that is exploited to identify an unknown nonlinearsystem via the standard gradient learning algorithm. The convergence of thisalgorithm for online training the three-layer neural networks in stochasticenvironment is studied. A special case where an unknown nonlinearity canexactly be approximated by some neural network with a nonlinear activationfunction for its output layer is considered. To analyze the asymptotic behaviorof the learning processes, the so-called Lyapunov-like approach is utilized. Asthe Lyapunov function, the expected value of the square of approximation errordepending on network parameters is chosen. Within this approach, sufficientconditions guaranteeing the convergence of learning algorithm with probability1 are derived. Simulation results are presented to support the theoreticalanalysis.

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