Lur’e Postnikov Lyapunov functional technique to global Mittag-Leffler stability of fractional-order neural networks with piecewise constant argument

Wang, Lifei; Wu, Huaiqin; Liu, Da‐Yan; Boutat, Driss; Chen, Yiming

doi:10.1016/j.neucom.2018.03.050

Cited by 30 publications

(15 citation statements)

References 36 publications

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“…Inspired by existing similar studies on both artificial and natural neural networks [20][21][22], for estimating the instability of perturbations (Butterfly Effect) we considered a "flavor" of the Lyapunov Function method, which supposes monitoring the evolution in time of two identical systems, separated by an infinitesimal dissimilarity in initial conditions. In the context of social sciences, one first difficulty comes from implementing an initial small perturbation.…”

Section: Lyapunov Functionmentioning

confidence: 99%

Application of Chaos Theory in the Assessment of Emotional Vulnerability and Emotion Dysregulation in Adults

2020

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In this work, we propose an interdisciplinary chaos analysis of emotion dysregulation (ED) and emotional vulnerability in adults. One of the main goals was the assessment of incongruences that occur in the evaluation of one’s own emotional dysregulation mechanisms in the presence of an extremely weak stimulus (Butterfly Effect). Thus, we considered a “flavor” of the Lyapunov Function method based on the assumption that the effort of answering to the test is itself a small perturbation. In this context, we calculated the “instability coefficient” Δ defined as the Euclidean distance between the pairs of vectors that include similar and reverted items of a test. The relationship between Δ, ED, and emotional characteristics as quality (positive/negative) and type (trait/state) was highlighted. We hypothesized that a higher level of Δ should be significantly related with a higher ED and with the type and the quality of emotions. The results suggest that Δ is significantly correlated with trait emotions (positively with negative emotions, and negatively with positive ones) and with ED. Moreover, Δ significantly predicts ED in adults. Thus, we consider that this approach is promising with respect to the evolution of emotional mechanisms across time. The presence of an initial instability to a weak perturbation might predict future abnormal emotional functioning, which could put at risk the mental or psychosomatic systems.

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Section: Lyapunov Functionmentioning

confidence: 99%

Application of Chaos Theory in the Assessment of Emotional Vulnerability and Emotion Dysregulation in Adults

2020

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“…e traditional integer-order theory is not suitable for FOSs because of its unique definition, so the researchers adopt two new methods to stabilize the FOS. e first solution is Lyapunov function, and the other is Laplace transformation to stabilize FOS [11][12][13][14][15]. In control analysis, it is necessary to make the state trajectory of the system follow the desired command.…”

Section: Introductionmentioning

confidence: 99%

T-S Fuzzy Control of Uncertain Fractional-Order Systems with Time Delay

Hao

Zhang

2021

Journal of Mathematics

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In this article, the adaptive control of uncertain fractional-order time-delay systems (FOTDSs) with external disturbances is discussed. A Takagi-Sugenu (T-S) fuzzy model with if-then rules is adopted to characterize the dynamic equation of the FOTDS. Besides, a fuzzy adaptive method is proposed to stabilize the model. By utilizing the Lyapunov functions, a robust controller is constructed to stabilize the FOTDS. Due to the uncertainty of system parameters, some fractional-order adaptation laws are designed to update these parameters. At the same time, some if-then rules with linear structure based on the fuzzy T-S adaption concept are established. The designed method not only guarantees that the state of closed-loop system asymptotically converges to origin but also keeps the signal in the FOTDS bounded. Finally, the applicability of the control method is proved by simulation examples.

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“…Thus, fractional-order artificial neural networks were developed in [1]. Since then, many properties of this type of networks were studied: asymptotic stability and synchronization [2][3][4][5][6][7], Mittag-Leffler stability and synchronization [8][9][10][11][12][13], dissipativity [14][15][16], etc.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

Popa

Kaslik

2020

Mathematics

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This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria.

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Lur’e Postnikov Lyapunov functional technique to global Mittag-Leffler stability of fractional-order neural networks with piecewise constant argument

Cited by 30 publications

References 36 publications

Application of Chaos Theory in the Assessment of Emotional Vulnerability and Emotion Dysregulation in Adults

Application of Chaos Theory in the Assessment of Emotional Vulnerability and Emotion Dysregulation in Adults

T-S Fuzzy Control of Uncertain Fractional-Order Systems with Time Delay

Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

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