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Some generalized sufficient convergence criteria for nonlinear continuous neural networks
Jito Vanualailai1, Shin-ichi Nakagiri
1Department of Mathematics and Computing Science, University of the South Pacific, Suva, Fiji. vanualailai@usp.ac.fi
Neural Computation
|June 23, 2005
Summary
This study simplifies designing stable artificial neural networks (ANNs) using Lyapunov functions. It introduces a systematic procedure to achieve global asymptotic stability, offering new insights and confirming existing convergence conditions.
Area of Science:
- Dynamical systems theory
- Artificial intelligence
- Control theory
Background:
- Artificial neural networks (ANNs) are increasingly complex, requiring robust stability analysis.
- The direct Lyapunov method is a key tool for designing stable dynamical neural networks.
- Existing Lyapunov functions (quadratic, Persidskii, Luré-Postnikov) have limitations.
Purpose of the Study:
- To revisit and generalize the use of quadratic Lyapunov functions for ANNs.
- To develop a simple and systematic procedure for ensuring global asymptotic stability in ANNs.
- To unify and derive known convergence conditions using a novel Lyapunov-based approach.
Main Methods:
- Application of the direct method of Lyapunov.
- Utilizing Krasovskii-like stability criteria.
- Revisiting and adapting quadratic Lyapunov functions.
Main Results:
- A simplified, systematic procedure for designing stable ANNs is presented.
- New and generalized results for ANN stability are obtained.
- Well-known sufficient conditions for convergence, established by non-Lyapunov methods, are derived.
Conclusions:
- The revisited quadratic Lyapunov function approach offers a powerful and unified framework for ANN stability analysis.
- This method provides a systematic way to achieve global asymptotic stability in dynamical neural networks.
- The findings bridge Lyapunov-based and non-Lyapunov methods for analyzing ANN convergence.
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