Tsypkin, Ya.Z., Mason, J.D., Avedyan, E.D., Warwick, K. and Levin, I.K. (1999) Neural Networks for Identification of Nonlinear Systems Under Random Piecewise Polynomial Disturbances. IEEE Transactions on Neural Networks, 10, 303-311.
https://doi.org/10.1109/72.750559

has been cited by the following article:

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

  AUTHORS: Leonid S. Zhiteckii, Valerii N. Azarskov, Sergey A. Nikolaienko, Klaudia Yu. Solovchuk

  KEYWORDS: Neural Network, Nonlinear Model, Online Learning Algorithm, Lyapunov Func-tion, Probabilistic Convergence

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.1, January 29, 2018

  ABSTRACT: This paper deals with deriving the properties of updated neural network model that is exploited to identify an unknown nonlinear system via the standard gradient learning algorithm. The convergence of this algorithm for online training the three-layer neural networks in stochastic environment is studied. A special case where an unknown nonlinearity can exactly be approximated by some neural network with a nonlinear activation function for its output layer is considered. To analyze the asymptotic behavior of the learning processes, the so-called Lyapunov-like approach is utilized. As the Lyapunov function, the expected value of the square of approximation error depending on network parameters is chosen. Within this approach, sufficient conditions guaranteeing the convergence of learning algorithm with probability 1 are derived. Simulation results are presented to support the theoretical analysis.