Global robust stability of delayed neural networks with discontinuous activation functions

2008 ◽  
Vol 2 (7) ◽  
pp. 543-553 ◽  
Author(s):  
Y. Wang ◽  
C. Li ◽  
Y. Zuo ◽  
L. Huang
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Activation Functions ◽  
Delayed Neural Networks ◽  
Discontinuous Activation ◽  
Global Robust Stability ◽  
Discontinuous Activation Functions

scholarly journals Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xinsong Yang ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Adaptive Control ◽  
Control Technique ◽  
Activation Functions ◽  
Complete Synchronization ◽  
Delayed Neural Networks ◽  
Discontinuous Activation ◽  
Discontinuous Activations ◽  
Discontinuous Activation Functions ◽  
Continuous Neural Networks

The drive-response synchronization of delayed neural networks with discontinuous activation functions is investigated via adaptive control. The synchronization of this paper means that the synchronization error approaches to zero for almost all time as time goes to infinity. The discontinuous activation functions are assumed to be monotone increasing which can be unbounded. Due to the mild condition on the discontinuous activations, adaptive control technique is utilized to control the response system. Under the framework of Filippov solution, by using Lyapunov function and chain rule of differential inclusion, rigorous proofs are given to show that adaptive control can realize complete synchronization of the considered model. The results of this paper are also applicable to continuous neural networks, since continuous function is a special case of discontinuous function. Numerical simulations verify the effectiveness of the theoretical results. Moreover, when there are parameter mismatches between drive and response neural networks with discontinuous activations, numerical example is also presented to demonstrate the complete synchronization by using discontinuous adaptive control.

Dynamical Behaviors of Delayed Neural Network Systems with Discontinuous Activation Functions

2006 ◽  
Vol 18 (3) ◽  
pp. 683-708 ◽  
Author(s):  
Wenlian Lu ◽  
Tianping Chen
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Activation Functions ◽  
Network Systems ◽  
Delayed Neural Networks ◽  
Discontinuous Activation ◽  
Feedback Matrix ◽  
Inequality Technique ◽  
Discontinuous Activation Functions

In this letter, without assuming the boundedness of the activation functions, we discuss the dynamics of a class of delayed neural networks with discontinuous activation functions. A relaxed set of sufficient conditions is derived, guaranteeing the existence, uniqueness, and global stability of the equilibrium point. Convergence behaviors for both state and output are discussed. The constraints imposed on the feedback matrix are independent of the delay parameter and can be validated by the linear matrix inequality technique. We also prove that the solution of delayed neural networks with discontinuous activation functions can be regarded as a limit of the solutions of delayed neural networks with high-slope continuous activation functions.

Robust stability of mixed Cohen–Grossberg neural networks with discontinuous activation functions

2019 ◽  
Vol 12 (1) ◽  
pp. 82-101 ◽  
Author(s):  
Cheng-De Zheng ◽  
Ye Liu ◽  
Yan Xiao
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Integral Inequality ◽  
Sufficient Condition ◽  
Activation Functions ◽  
Content Type ◽  
Alternative Theorem ◽  
Discontinuous Activation ◽  
Discontinuous Activation Functions ◽  
Delay Dependent

PurposeThe purpose of this paper is to develop a method for the existence, uniqueness and globally robust stability of the equilibrium point for Cohen–Grossberg neural networks with time-varying delays, continuous distributed delays and a kind of discontinuous activation functions.Design/methodology/approachBased on the Leray–Schauder alternative theorem and chain rule, by using a novel integral inequality dealing with monotone non-decreasing function, the authors obtain a delay-dependent sufficient condition with less conservativeness for robust stability of considered neural networks.FindingsIt turns out that the authors’ delay-dependent sufficient condition can be formed in terms of linear matrix inequalities conditions. Two examples show the effectiveness of the obtained results.Originality/valueThe novelty of the proposed approach lies in dealing with a new kind of discontinuous activation functions by using the Leray–Schauder alternative theorem, chain rule and a novel integral inequality on monotone non-decreasing function.

Sign in / Sign up

Export Citation Format

Share Document