Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem

Xue Bin Liang, Jennie Si

Research output: Contribution to journalArticle

80 Scopus citations

Abstract

This paper investigates the existence, uniqueness, and global exponential stability (GES) of the equilibrium point for a large class of neural networks with globally Lipschitz continuous activations including the widely used sigmoidal activations and the piecewise linear activations. The provided sufficient condition for GES is mild and some conditions easily examined in practice are also presented. The GES of neural networks in the case of locally Lipschitz continuous activations is also obtained under an appropriate condition. The analysis results given in the paper extend substantially the existing relevant stability results in the literature, and therefore expand significantly the application range of neural networks in solving optimization problems. As a demonstration, we apply the obtained analysis results to the design of a recurrent neural network (RNN) for solving the linear variational inequality problem (VIP) defined on any nonempty and closed box set, which includes the box constrained quadratic programming and the linear complementarity problem as the special cases. It can be inferred that the linear VIP has a unique solution for the class of Lyapunov diagonally stable matrices, and that the synthesized RNN is globally exponentially convergent to the unique solution. Some illustrative simulation examples are also given.

Original languageEnglish (US)
Pages (from-to)349-359
Number of pages11
JournalIEEE Transactions on Neural Networks
Volume12
Issue number2
DOIs
StatePublished - Mar 1 2001

Keywords

  • Global Lipschitz continuous activations
  • Global exponential stability
  • Linear variational inequality problems
  • Recurrent neural networks

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence

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