Dongbing Tong

Stability and Synchronization Control of Stochastic Neural Networks

This bookreports on the latest findings in the study of Stochastic Neural Networks (SNN). The book collects the novel model of the disturbance driven by Levy process, the research method of M-matrix, and the adaptive control method of the SNN in the context of stability and synchronization control. The book will be of interest to university researchers, graduate students in control science and engineering and neural networks who wish to learn the core principles, methods, algorithms and applications of SNN.

Stability Analysis and Application for Delayed Neural Networks Driven by Fractional Brownian Noise

This paper deals with two types of the stability problem for the delayed neural networks driven by fractional Brownian noise (FBN). The existence and the uniqueness of the solution to the main system with respect to FBN are proved via fixed point theory. Based on Hilbert–Schmidt operator theory and analytic semigroup principle, the mild solution of the stochastic neural networks is obtained. By applying the stochastic analytic technique and some well-known inequalities, the asymptotic stability criteria and the exponential stability condition are established. Both numerical example and practical application for synchronization control of multiagent system are provided to illustrate the effectiveness and potential of the proposed techniques.

Stability analysis based on partition trajectory approach for switched neural networks with fractional Brown noise disturbance

ABSTRACT In this brief, the stability problem based on feedback control for two types of stochastic neural networks driven by fractional Brown noise is considered. One class is the switched neural networks without time delays and the other one is with time delays. A novel analysis method, very different to the usual approach based on the Itô formula and infinitesimal operator, is proposed in this paper. By the idea of splitting time of trajectory and associating with hölder inequality, some criteria are obtained to guarantee the switched neural networks with two types to be stable. In the end, two numerical examples and auxiliary figures are presented to show the feasibility and effectiveness for the proposed results.

pth Moment synchronization of Markov switched neural networks driven by fractional Brownian noise

This paper deals with the pth moment synchronization problem for a type of the stochastic neural networks with Markov switched parameters and driven by fractional Brownian noise (FBNSNN). A method called time segmentation method, very different to the Lyapunov functional approach, has been presented to solve the above problem. Meanwhile, based on the trajectory of error system, associating with infinitesimal operator theory, we propose a sufficient condition of consensus for the drive–response system. The criterion of pth moment exponential stability for FBNSNN can guarantee the synchronization under the designed controller. Finally, two numerical examples and some illustrative figures are provided to show the feasibility and effectiveness for our theoretical results.

Stability and Synchronization of Neutral-Type Neural Networks

When the states of a system are decided not only by states of the current time and the past time but also by the derivative of the past states, the system can be called a neutral system. The problems of stability and synchronization of neutral neural networks play an important role in the same issues of neural networks. In this chapter, robust stability of neutral neural networks is first discussed.

Some Applications to Economy Based on Related Research Method

This chapter provides two applications with respect to the topic of this book in finance and economy. As an application of Levy process, Sect. 7.1 offers a portfolio strategy of financial market. Robust \(H_\infty \) control strategy is investigated for a generic linear rational expectation model of economy.

Adaptive Synchronization of Neural Networks

The adaptive control strategy has been widely adopted due to its well performance in uncertain systems such as stochastic systems or nonlinear systems. In this chapter, adaptive control is designed for the synchronization of some kinds of neural networks including BAMDNN, SDNN with Markovian switching and T-S fuzzy NN.

Relative Mathematic Foundation

In this chapter, we will present some concepts and formulas as well as several important inequalities which will be used throughout this book. We will begin with some elementary concepts and formulas, such as stochastic processes and martingales, SDEs, M-matrix, and Ito’s formula. Then some inequalities frequently used in this book will follow in the sequel.

Exponential Stability and Synchronization Control of Neural Networks

In this chapter, we are concerned with exponential stability analysis for neural networks with fuzzy logical BAM and Markovian jump and synchronization control problem of stochastically coupled neural networks.

Robust Stability and Synchronization of Neural Networks

In this chapter, the robust stability of high-order neural networks and hybrid stochastic neural networks is first investigated. The robust anti-synchronization and robust lag synchronization of chaotic neural networks are discussed in the sequel.