New stability and stabilization conditions for stochastic neural networks of neutral type with Markovian jumping parameters

Wu, Tao; Xiong, Lianglin; Cao, Jinde; Liu, Zixin; Zhang, Haiyang

doi:10.1016/j.jfranklin.2018.09.032

Cited by 34 publications

(10 citation statements)

References 35 publications

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“…Hence, the stability of stochastic neural networks (SNNs) has attained persistent attention among the research communities. In recent years, vast quantity of significant results on SNNs with time‐varying delays have been discussed (see, for instance, References 9‐14). Particularly, the authors in Reference 9 inspected the finite‐time synchronization problem for a class of nonlinear SNNs subject to time‐delay and noise disturbance.…”

Section: Introductionmentioning

confidence: 99%

Observer‐based guaranteed cost control for IT‐2 stochastic fuzzy coupled neural networks with Markov switching topology

Arumugam

Sakthivel

Liu

2022

Adaptive Control & Signal

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Summary This study focuses on the guaranteed cost control problem for interval type‐2 stochastic fuzzy coupled neural networks (NNs) elicited by the observer framework with Markov switching topology, external disturbances, and quantization effect. In particular, the guaranteed cost controller is developed with an upper bound of the guaranteed cost function and also ensures stability of the addressed networks. Also, the integration of lower and upper membership functions are incorporated to relax the stability condition of the networks. Notably, the randomness phenomena are incorporated by the agency of stochastic variables that satisfies the Bernoulli distribution characteristics. Specifically, the state feedback controller considered with quantization effect is designed through undirected communication graph subject to Markov switching topology. In consequence with Lyapunov–Krasovskii‐functional and algebraic graph theory, sufficient conditions are established to assure the stochastic stabilization of the NNs with some specified cost value. Explicitly, the optimal upper bound of the guaranteed cost function and the controller gain fluctuations of the state and the observer are effectuated through the developed conditions. Finally, the reduced conservatism and efficiency of the proposed analytical design are demonstrated through a numerical example.

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Section: Introductionmentioning

confidence: 99%

Observer‐based guaranteed cost control for IT‐2 stochastic fuzzy coupled neural networks with Markov switching topology

Arumugam

Sakthivel

Liu

2022

Adaptive Control & Signal

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“…Li et al [2] studied the problem of event-triggered control, which applied nonlinear continuous-time systems under strict-feed-back condition. Tao et al [3] analyzed the stability conditions for stochastic neural networks with Markovian jumping parameters, but the designed Markovian process is complex, furthermore, it improved the complexity of solution. Because the time-dependent Lyapunov function owns the ability of capturing the information that presents the feature of time-varying delays, the conditions derived of Lyapunov functional were less open.…”

Section: Introductionmentioning

confidence: 99%

Approach with Reducing Time-Delays to Rise Prediction Ability for Neural Networks

Zheng¹,

Li²,

He³

2021

dtcse

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The time-delays induce instability, then the instability influences the prediction accuracy of neural networks, hence, time-delays should be considered as a key indicator for constructing neural networks. Based on above mentioned problem, we reconstructed time-dependent Lyapunov function. Next following, we found the sufficient condition which ensured the convergence of neural networks and prevented highfrequency oscillation, which effectively increased the prediction accuracy of neural networks. This results show that the prediction accuracy about raise 2.5% for neural networks after reducing time-delays, and the mean square error decreased about 0.02 for training samples using neural networks.

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“…On the contrary, in the real world, the Markov jump usually exists in chaotic systems since the abrupt changes in their structure and parameters. So, the study on chaotic systems with Markov jump parameters is of great importance [29][30][31]. It is noted that the transition rates in the aforementioned works are always supposed to be totally known.…”

Section: Introductionmentioning

confidence: 99%

New Stabilization Results for Semi‐Markov Chaotic Systems with Fuzzy Sampled‐Data Control

Cao

Xiong

et al. 2019

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This paper investigates the problem of stabilization for semi-Markov chaotic systems with fuzzy sampled-data controllers, in which the semi-Markov jump has generally uncertain transition rates. The exponential stability condition is firstly obtained by the following two main techniques: To make full use of the information about the actual sampling pattern, a novel augmented input-delay-dependent Lyapunov–Krasovskii functional (LKF) is firstly introduced. Meanwhile, a new zero-value equation is established to increase the combinations of component vectors of the resulting vector. The corresponding fuzzy sampled-data controllers are designed based on the stability condition. Finally, the validity and merits of the developed theories are shown by two numerical examples.

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New stability and stabilization conditions for stochastic neural networks of neutral type with Markovian jumping parameters

Cited by 34 publications

References 35 publications

Observer‐based guaranteed cost control for IT‐2 stochastic fuzzy coupled neural networks with Markov switching topology

Observer‐based guaranteed cost control for IT‐2 stochastic fuzzy coupled neural networks with Markov switching topology

Approach with Reducing Time-Delays to Rise Prediction Ability for Neural Networks

New Stabilization Results for Semi‐Markov Chaotic Systems with Fuzzy Sampled‐Data Control

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