Sequential learning processes in neural networks applied as models of nonlinear systems

Azarskov, Valerii N.; Zhiteckii, Leonid S.; Nikolaienko, Sergii A.

doi:10.18372/1990-5548.37.6506

Cited by 1 publication

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“…Then { } n V will converge with probability 1 (a.s.) for any (0) w provided that the condition (26) (27) it can conclude that there exists a finite number n * < ∞ such that χn = 0 for all n ≥ n*. Since {χn} is nonnegative, this gives (25) follows.…”

Section: Preliminariesmentioning

confidence: 87%

“…It turned out that, at least, in the ideal case, the set , W * containing these s w * becomes not one-point [26,27] …”

Section: Preliminariesmentioning

confidence: 99%

“…This approach has been exploited in [26,27] to derive some local convergence in stochastic framework for standard online gradient algorithms with the constant learning rate.…”

Section: Introductionmentioning

confidence: 99%

“…This paper is an extension of [26,27]. The main efforts is focused on establishing sufficient conditions under which the global convergence of gradient algorithm for learning neural networks models in the stochastic environments is ensured.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems

Azarskov¹,

Kucherov²,

Nikolaienko³

et al. 2015

AJNNA

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This paper deals with studying the asymptotical properties of multilayer neural networks models used for the adaptive identification of wide class of nonlinearly parameterized systems in stochastic environment. To adjust the neural network's weights, the standard online gradient type learning algorithms are employed. The learning set is assumed to be infinite but bounded. The Lyapunov-like tool is utilized to analyze the ultimate behaviour of learning processes in the presence of stochastic input variables. New sufficient conditions guaranteeing the global convergence of these algorithms in the stochastic frameworks are derived. The main their feature is that they need no a penalty term to achieve the boundedness of weight sequence. To demonstrate asymptotic behaviour of the learning algorithms and support the theoretical studies, some simulation examples are also given.

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Section: Preliminariesmentioning

confidence: 87%

“…It turned out that, at least, in the ideal case, the set , W * containing these s w * becomes not one-point [26,27] …”

Section: Preliminariesmentioning

confidence: 99%

“…This approach has been exploited in [26,27] to derive some local convergence in stochastic framework for standard online gradient algorithms with the constant learning rate.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations