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Improved Passivity Analysis for Neural Networks With Time-Varying Delay.

Xi-Zi Zhou, Jianqi An, Yong He

IEEE Transactions on Cybernetics

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Summary

This study introduces a new method for analyzing neural networks with time-varying delays (NNTVDs), enhancing stability criteria. The approach simplifies complex terms, leading to less conservative passivity and stability conditions for NNTVDs.

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A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

Area of Science:

Control Theory
Artificial Intelligence
Dynamical Systems

Background:

Neural networks with time-varying delays (NNTVDs) present significant analytical challenges.
Estimating the derivative of the Lyapunov-Krasovskii functional (LKF) in NNTVDs involves complex nonlinear delay-dependent terms.
Existing methods for passivity analysis in NNTVDs can be overly conservative.

Purpose of the Study:

To develop a novel method for the passivity analysis of neural networks with time-varying delays (NNTVDs).
To overcome the challenge of nonlinear delay-dependent terms in LKF derivative estimation.
To derive less conservative passivity and stability criteria for NNTVDs.

Main Methods:

A linearization variable augmentation method using zero equations and time-varying free-weighting matrices.
Incorporation of the delay derivative into the augmentation method to eliminate nonlinear terms.
An improved time-varying S-procedure with multiplier matrices as affine functions of delay, its derivative, and their product.

Main Results:

The proposed method completely eliminates nonlinear delay terms, making the passivity condition affine with respect to the delay.
The improved S-procedure allows greater freedom in bounding neuron activation functions.
Novel passivity and stability criteria for NNTVDs are established that are significantly less conservative than existing approaches.

Conclusions:

The developed techniques provide a more effective framework for analyzing the passivity and stability of neural networks with time-varying delays.
Comparative numerical examples and a case study validate the reduced conservatism and improved performance of the proposed criteria.
This work offers advancements in control theory for complex dynamical systems involving time delays.