Fixed-Time Synchronization of Delayed Memristive Neural Networks with Discontinuous Activations

Hao Pu,Fengjun Li,Niansheng Tang

doi:10.1155/2021/3350534

Hao Pu, Fengjun Li + Show 1 more

Open Access

https://doi.org/10.1155/2021/3350534

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Abstract

In this paper, the fixed-time synchronization problem for a class of memristive neural networks with discontinuous neuron activation functions and mixed time-varying delays is investigated. With the help of the fixed-time stability theory, under the framework of Filippov solution and differential inclusion theory, several new and useful sufficient criteria for fixed-time synchronization are obtained by designing two types of energy-saving and simple controllers for the considered systems. Compared with the traditional fixed-time synchronization controller, the controllers used in this paper only have one power exponent term, which is a function of the system state error rather than a constant. Moreover, some previous relevant works are especially improved. Finally, two numerical examples are given to show the correctness and the effectiveness of the obtained theoretical results.

Highlights

Problem Formulation and PreliminariesA class of memristive neural networks are considered with discontinuous activation functions and mixed time-varying delays described by the following equation:
It is not hard to notice that, from the previous literature review, many published works on neural network synchronization focused on the hypothesis that the activation function should be continuous, bounded, or even global Lipschitz
The discrete-time delays and distributed delays often affect the stability of the neural network system and may lead to some complex dynamic behaviors, such as instability, chaos, and oscillation. us, the synchronization of memristive neural networks with mixed time-varying delays has been widely concerned [37,38,39]. e global synchronization of fuzzy memristive neural networks with discrete and distributed delays was investigated in [37] based on the nonsmooth analysis and Lyapunov stability theory. e synchronization of memristive neural networks with mixed time delays was discussed under a quantized intermittent control in [39] with weighted double-integral inequalities and novel Lyapunov-Krasovskii functionals

Summary

Problem Formulation and Preliminaries

A class of memristive neural networks are considered with discontinuous activation functions and mixed time-varying delays described by the following equation:. (H4) ∀u, v ∈ R, there exist positive constants Lj and Zj such that the continuous neuron activation functions fj(·) and gj(·) satisfy. Due to the memristive connection weights ai(·), bij(·), cij(·), and dij(·) and the fact that the activation functions fj(·) and gi(·) of the drive-response systems (1) and (8) are discontinuous, the classic solution is not suitable for the drive-response systems (1) and (8). If the assumptions (H1) and (H2) hold, according to Definition 1, we know that xi(t) and yi(t) are the Filippov sense solutions of the drive system (1) and the response system (8), respectively, where i ∈ I. − sign yi(t) − xi(t)􏼁 a i(t)yi(t) − a􏽥i(t)xi(t)􏼁 ≤ − ai􏼌􏼌􏼌􏼌ei(t)􏼌􏼌􏼌􏼌 +􏼌􏼌􏼌􏼌a∗i − ai∗ ∗ 􏼌􏼌􏼌􏼌Ti

Main Results

Numerical Simulations

Conclusions