Finite-time stochastic synchronization of fuzzy bi-directional associative memory neural networks with Markovian switching and mixed time delays via intermittent quantized control

Chengqiang Wang; Xiangqing Zhao; Yang Wang; Chengqiang Wang; Xiangqing Zhao; Yang Wang

doi:10.3934/math.2023204

AIMS Mathematics

2023, Volume 8, Issue 2: 4098-4125. doi: 10.3934/math.2023204

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Research article

Finite-time stochastic synchronization of fuzzy bi-directional associative memory neural networks with Markovian switching and mixed time delays via intermittent quantized control

1.
School of Mathematics, Suqian University, Suqian 223800, China
2.
Public Class Teaching Department, Sichuan Vocational and Technical College of Communications, Chengdu 611130, China

Received: 11 September 2022 Revised: 20 November 2022 Accepted: 27 November 2022 Published: 01 December 2022
MSC : 93E15, 28E10, 34K20, 34K37, 34K50, 60H10

We are concerned in this paper with the finite-time synchronization problem for fuzzy bi-directional associative memory neural networks with Markovian switching, discrete-time delay in leakage terms, continuous-time and infinitely distributed delays in transmission terms. After detailed analysis, we come up with an intermittent quantized control for the concerned bi-directional associative memory neural network. By designing an elaborate Lyapunov-Krasovskii functional, we prove under certain additional conditions that the controlled network is stochastically synchronizable in finite time: The $ 1 $st moment of every trajectory of the error network system associated to the concerned controlled network tends to zero as time approaches a finite instant (the settling time) which is given explicitly, and remains to be zero constantly thereupon. In the meantime, we present a numerical example to illustrate that the synchronization control designed in this paper is indeed effective. Since the concerned fuzzy network includes Markovian jumping and several types of delays simultaneously, and it can be synchronized in finite time by our suggested control, as well as the suggested intermittent control is quantized which could reduce significantly the control cost, the theoretical results in this paper are rich in mathematical implication and have wide potential applicability in the real world.
- finite-time synchronization,
- fuzzy bi-directional associative memory neural networks,
- mixed time delays,
- Markovian jumping,
- intermittent quantized control
Citation: Chengqiang Wang, Xiangqing Zhao, Yang Wang. Finite-time stochastic synchronization of fuzzy bi-directional associative memory neural networks with Markovian switching and mixed time delays via intermittent quantized control[J]. AIMS Mathematics, 2023, 8(2): 4098-4125. doi: 10.3934/math.2023204

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Abstract

We are concerned in this paper with the finite-time synchronization problem for fuzzy bi-directional associative memory neural networks with Markovian switching, discrete-time delay in leakage terms, continuous-time and infinitely distributed delays in transmission terms. After detailed analysis, we come up with an intermittent quantized control for the concerned bi-directional associative memory neural network. By designing an elaborate Lyapunov-Krasovskii functional, we prove under certain additional conditions that the controlled network is stochastically synchronizable in finite time: The $ 1 $st moment of every trajectory of the error network system associated to the concerned controlled network tends to zero as time approaches a finite instant (the settling time) which is given explicitly, and remains to be zero constantly thereupon. In the meantime, we present a numerical example to illustrate that the synchronization control designed in this paper is indeed effective. Since the concerned fuzzy network includes Markovian jumping and several types of delays simultaneously, and it can be synchronized in finite time by our suggested control, as well as the suggested intermittent control is quantized which could reduce significantly the control cost, the theoretical results in this paper are rich in mathematical implication and have wide potential applicability in the real world.

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