Stability Analysis and the Stabilization of a Class of Discrete-Time Dynamic Neural Networks

Abstract

This paper deals with problems of stability and the stabilization of discrete-time neural networks. Neural structures under consideration belong to the class of the so-called locally recurrent globally feedforward networks. The single processing unit possesses dynamic behavior. It is realized by introducing into the neuron structure a linear dynamic system in the form of an infinite impulse response filter. In this way, a dynamic neural network is obtained. It is well known that the crucial problem with neural networks of the dynamic type is stability as well as stabilization in learning problems. The paper formulates stability conditions for the analyzed class of neural networks. Moreover, a stabilization problem is defined and solved as a constrained optimization task. In order to tackle this problem two methods are proposed. The first one is based on a gradient projection (GP) and the second one on a minimum distance projection (MDP). It is worth noting that these methods can be easily introduced into the existing learning algorithm as an additional step, and suitable convergence conditions can be developed for them. The efficiency and usefulness of the proposed approaches are justified by using a number of experiments including numerical complexity analysis, stabilization effectiveness, and the identification of an industrial process.

EKF Based Generalized Predictive Control of Nonlinear Systems

“…The results in [7,10] were reviewed to analyse the stability of the models and stability conditions given in [15] were followed in this study. as the initial state is obtained as follows.…”

Local stability conditions for discrete-time cascade locally recurrent neural networks

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Towards Robustness in Neural Network Based Fault Diagnosis

“…Artificial Neural Networks (ANNs) have been intensively studied during the last two decades and successfully applied to dynamic system modelling and fault diagnosis (Narendra and Parthasarathy, 1990;Frank and Köppen-Seliger, 1997;Köppen-Seliger and Frank, 1999;Korbicz et al, 2004;Korbicz, 2006;Witczak, 2006;Patan, 2007c). Neural networks stand for an interesting and valuable alternative to the classical methods, because they can deal with very complex situations which are not sufficiently defined for deterministic algorithms.…”