Stability and convergence analysis for a class of neural networks

Xingbao Gao; Lizhi LIAO

doi:10.1109/TNN.2011.2167760

Stability and convergence analysis for a class of neural networks

Xingbao Gao^*, Lizhi LIAO

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

4 Citations (Scopus)

Abstract

In this paper, we analyze and establish the stability and convergence of the dynamical system proposed by Xia and Feng, whose equilibria solve variational inequality and related problems. Under the pseudo-monotonicity and other conditions, this system is proved to be stable in the sense of Lyapunov and converges to one of its equilibrium points for any starting point. Meanwhile, the global exponential stability of this system is also shown under some mild conditions without the strong monotonicity of the mapping. The obtained results improve and correct some existing ones. The validity and performance of this system are demonstrated by some numerical examples.

Original language	English
Article number	6031924
Pages (from-to)	1770-1782
Number of pages	13
Journal	IEEE Transactions on Neural Networks
Volume	22
Issue number	11
DOIs	https://doi.org/10.1109/TNN.2011.2167760
Publication status	Published - Nov 2011

Scopus Subject Areas

Software
Computer Science Applications
Computer Networks and Communications
Artificial Intelligence

User-Defined Keywords

Convergence
exponential stability
neural network
variational inequality

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10.1109/TNN.2011.2167760

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title = "Stability and convergence analysis for a class of neural networks",

abstract = "In this paper, we analyze and establish the stability and convergence of the dynamical system proposed by Xia and Feng, whose equilibria solve variational inequality and related problems. Under the pseudo-monotonicity and other conditions, this system is proved to be stable in the sense of Lyapunov and converges to one of its equilibrium points for any starting point. Meanwhile, the global exponential stability of this system is also shown under some mild conditions without the strong monotonicity of the mapping. The obtained results improve and correct some existing ones. The validity and performance of this system are demonstrated by some numerical examples.",

keywords = "Convergence, exponential stability, neural network, variational inequality",

author = "Xingbao Gao and Lizhi LIAO",

note = "Funding Information: Manuscript received February 16, 2011; revised May 29, 2011; accepted September 2, 2011. Date of publication September 29, 2011; date of current version November 2, 2011. This work was supported in part by the National Science Foundation of China under Grant 60671063 and Grant 10902062, the Hong Kong Baptist University, and the Research Grant Council of Hong Kong.",

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T1 - Stability and convergence analysis for a class of neural networks

AU - Gao, Xingbao

AU - LIAO, Lizhi

N1 - Funding Information: Manuscript received February 16, 2011; revised May 29, 2011; accepted September 2, 2011. Date of publication September 29, 2011; date of current version November 2, 2011. This work was supported in part by the National Science Foundation of China under Grant 60671063 and Grant 10902062, the Hong Kong Baptist University, and the Research Grant Council of Hong Kong.

PY - 2011/11

Y1 - 2011/11

N2 - In this paper, we analyze and establish the stability and convergence of the dynamical system proposed by Xia and Feng, whose equilibria solve variational inequality and related problems. Under the pseudo-monotonicity and other conditions, this system is proved to be stable in the sense of Lyapunov and converges to one of its equilibrium points for any starting point. Meanwhile, the global exponential stability of this system is also shown under some mild conditions without the strong monotonicity of the mapping. The obtained results improve and correct some existing ones. The validity and performance of this system are demonstrated by some numerical examples.

AB - In this paper, we analyze and establish the stability and convergence of the dynamical system proposed by Xia and Feng, whose equilibria solve variational inequality and related problems. Under the pseudo-monotonicity and other conditions, this system is proved to be stable in the sense of Lyapunov and converges to one of its equilibrium points for any starting point. Meanwhile, the global exponential stability of this system is also shown under some mild conditions without the strong monotonicity of the mapping. The obtained results improve and correct some existing ones. The validity and performance of this system are demonstrated by some numerical examples.

KW - Convergence

KW - exponential stability

KW - neural network

KW - variational inequality

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JO - IEEE Transactions on Neural Networks and Learning Systems

JF - IEEE Transactions on Neural Networks and Learning Systems

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Stability and convergence analysis for a class of neural networks

Abstract

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