Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays

Su, Weiwei; Chen, Yiming

doi:10.1016/j.cnsns.2008.05.001

Cited by 20 publications

(6 citation statements)

References 28 publications

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“…La presencia de factores inevitables, como es el error de modelado, aparición inesperada de perturbaciones externas y la fluctuación de parámetros durante la implementación física, inducen a las redes neuronales incertidumbres y variaciones en los componentes, que afectan considerablemente la pasividad del sistema completo. En este sentido, con el fin de analizar la incertidumbre que puede llegar a ser inducida en una red neuronal, se han propuesto procedimientos simples que consisten en asumir parámetros en ciertos intervalos [73], [74]. Es importante resaltar que la teoría de pasividad fue originada del análisis de circuitos y se ha convertido en una herramienta útil para analizar la estabilidad de los sistemas [75].…”

Section: Modelos Neuro-difusos Para Sistemas Estocásticos Con Infounclassified

Dinámica Estocástica o Compleja con Información Incompleta: Una Revisión desde el Control

Gómez¹,

Palacio²,

Valencia³

et al. 2013

Iteckne

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Resumen-El control de procesos con dinámica estocástica o compleja es exitoso siempre y cuando se pueda estimar un modelo que se ajuste bien al comportamiento, sin embargo, esta suposición pierde validez en aplicaciones donde la información del sistema es reducida o incompleta, muy comunes en ambientes reales de la industria. La literatura presenta diferentes esquemas de control, siendo los modelos neuro-difusos los que reportan mejor desempeño. Estos modelos conjugan la capacidad de adaptación que tienen las redes neuronales con la robustez de los motores de inferencia que tiene la lógica difusa, para modelar el conocimiento de expertos mediante reglas de aprendizaje, identificar dinámicas complejas y aumentar la adaptabilidad del sistema a perturbaciones que en la práctica tienden a ser de naturaleza estocástica sumado, a veces, que la información del sistema sea restringida. Este artículo presenta una revisión sobre dificultades y soluciones derivadas del control de sistemas estocásticos o complejos con información incompleta. Se revisan las estructuras de control cuando la dinámica del sistema presenta vaguedad en los datos, la evolución hacia técnicas adaptativas, y el desempeño de las redes neuro-difusas ante procesos estocásticos o complejos con incertidumbre en los datos. De forma preliminar se establece que el control de este tipo de sistemas debe estar compuesto por modelos híbridos soportados en rutinas de optimización y análisis probabilístico que garanticen el tratamiento de las incertidumbres sin afectar el desempeño de las estructuras de control y la consistencia en la precisión.Palabras clave-Control adaptativo, sistemas estocás-ticos, redes neuronales, lógica difusa, modelos neurodifusos, información incompleta.Abstract-Control theory for processes with stochastic or complex dynamics has a successful performance as long as a model can be adjusted to the system behavior, although for real applications in the industry, where data can be reduced or incomplete, this statement may not be true. Different control schemes have been proposed and the literature reports promising results with neural fuzzy models. These models combine the adaptability of neural networks with the robust inference of fuzzy logic, in order to model expert knowledge by learning rules, identify complex dynamics and enhance the control adaptability when stochastic disturbances are present, which sometimes cause incomplete system data. This paper presents a review on the difficulties and solutions related to the control of stochastic or complex systems with incomplete data. This study, initially, discusses the control structures when the system data present notable uncertainty levels. Next, different adaptive control schemes are presented, and finally, nonlinear and stochastic control approaches based on neural fuzzy systems are reviewed. Thereby, in a preliminary way, this review establishes that a system under the conditions mentioned above should be controlled by hybrid models supported on probabilistic routines and optimizatio...

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Section: Modelos Neuro-difusos Para Sistemas Estocásticos Con Infounclassified

Dinámica Estocástica o Compleja con Información Incompleta: Una Revisión desde el Control

Gómez¹,

Palacio²,

Valencia³

et al. 2013

Iteckne

View full text Add to dashboard Cite

show abstract

“…To the best of our knowledge, few authors have considered the global exponential stability for model (1) with time-varying delays. Moreover, it should be noted that the assumptions of the activation functions in Theorems 1 and 2 are more general and different from those in [2,7,11,18,33]. In fact, we do not require that activation functions be bounded.…”

Section: Remarkmentioning

confidence: 99%

“…Particularly, the authors [3,8,9,14] had studied the stability of neural networks with time-varying delays. Very recently, in [17][18][19], the global exponential stability or robust H 1 state estimation problem is investigated for a class of stochastic interval neural networks with time-varying delays or with probabilistic measurement delays. In addition to the fact that global exponential stability implies global asymptotic stability, results leading to global exponential stability can provide relevant estimates on how fast such networks perform during real-time computations.…”

Section: Introductionmentioning

confidence: 99%

Global exponential stability analysis for a class of neural networks with time delays

Guo

Liu

2011

Intl J Robust & Nonlinear

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Employing Brouwer's fixed point theorem, matrix theory, we made a further investigation of a class of neural networks with delays in this paper. A family of sufficient conditions were given for checking global exponential stability. These results have important leading significance in the design and applications of globally stable neural networks with delays. Our results extended and improved some earlier publications.EXPONENTIAL STABILITY ANALYSIS FOR NEURAL NETWORKS WITH TIME DELAYS 1485As pointed out in [8], global dissipativity is also an important concept in dynamical neural networks. The concept of global dissipativity in dynamical systems is a more general concept, and it has found applications in areas such as stability theory, chaos and synchronization theory, system norm estimation, and robust control. Global dissipativity of several classes of neural networks were discussed and some sufficient conditions for the global dissipativity of neural networks with constant delays are derived in [8].In this paper, without assuming the boundedness, monotonicity, and differentiability of activation functions, we consider the following delay differential equation:

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“…By introducing a transformation of the interval matrices into norm-bounded uncertainties, the authors in [18] study the robust stability of the interval neural networks. In [33], delay-independent global exponential stability is investigated for a class of stochastic interval neural networks (SINNs) with time-varying delays. To the best of our knowledge, there are few results about the problem of dependent-range-dependent robust stability analysis for SINNs with discrete and distributed time-varying delays, which motivates this research.…”

Section: Introductionmentioning

confidence: 99%

Robust Stability for Interval Stochastic Neural Networks with Time-Varying Discrete and Distributed Delays

Cheung

Lam

et al. 2011

Differ Equ Dyn Syst

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This paper investigates the problem of robust stability for a class of stochastic interval neural networks with discrete and distributed time-varying delays. The discrete delays are assumed to be varying within a given interval, while the parameter uncertainties are assumed to be bounded in some given compact sets. Based on the Itô differential formula and stochastic stability theory, delay-range-dependent criteria for stochastic interval neural networks with time-varying delays are derived to guarantee robust global asymptotic stability in mean square. In this paper, when estimating the upper bound of the derivative of Lyapunov functionals, we are concerned with better handling of terms related to the discrete and distributed delays and establishing less conservative results. These robust stability conditions are presented in terms of linear matrix inequalities and can be efficiently solved via standard numerical software. An important feature of the results proposed in this paper is that the stability conditions are dependent on the upper and lower bounds of the discrete delays. Numerical examples are given to illustrate the effectiveness of the proposed method.

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Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays

Cited by 20 publications

References 28 publications

Dinámica Estocástica o Compleja con Información Incompleta: Una Revisión desde el Control

Dinámica Estocástica o Compleja con Información Incompleta: Una Revisión desde el Control

Global exponential stability analysis for a class of neural networks with time delays

Robust Stability for Interval Stochastic Neural Networks with Time-Varying Discrete and Distributed Delays

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