Stability And Synchronization Control Of Stochastic Neural Networks

This book reports 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.

This book provides up-to-date developments in the stability analysis and (anti-)synchronization control area for complex-valued neural networks systems with time delay. It brings out the characteristic systematism in them and points out further insight to solve relevant problems. It presents a comprehensive, up-to-date, and detailed treatment of dynamical behaviors including stability analysis and (anti-)synchronization control. The materials included in the book are mainly based on the recent research work carried on by the authors in this domain. The book is a useful reference for all those from senior undergraduates, graduate students, to senior researchers interested in or working with control theory, applied mathematics, system analysis and integration, automation, nonlinear science, computer and other related fields, especially those relevant scientific and technical workers in the research of complex-valued neural network systems, dynamic systems, and intelligent control theory.

This monograph studies the synchronization control of Markovian complex neural networks with time-varying delays, and the structure of the book is summarized as follows. Chapter 1 introduces the system description and some background knowledges, and also addresses the motivations of this monograph. In Chapter 2, the stochastic synchronization issue of Markovian coupled neural networks with partially unknown transition rates and random coupling strengths is investigated. In Chapter 3, the local synchronization issue of Markovian neutral complex networks with partially information of transition rates is investigated. The new delay-dependent synchronization criteria in terms of LMIs are derived, which depends on the upper and lower bounds of the delays. In Chapter 4, the local synchronization issue of Markovian nonlinear coupled neural networks with uncertain and partially unknown transition rates is investigated. The less conservative local synchronization criteria containing the bounds of delay and delay derivative are obtained based on the novel augmented Lyapunov-Krasovskii functional and a new integral inequality. In Chapter 5, the sampled-data synchronization issue of delayed complex networks with aperiodic sampling interval is investigated based on enhanced input delay approach, which makes full use of the upper bound of the variable sampling interval and the sawtooth structure information of varying input delay. In Chapter 6, the sampled-data synchronization issue of Markovian coupled neural networks with mode-dependent interval time-varying delays and aperiodic sampling intervals is investigated based on an enhanced input delay approach. Furthermore, the mode-dependent sampled-data controllers are proposed based on the delay dependent synchronization criteria. In Chapter 7, the synchronization issue of inertial neural networks with time-varying delays and generally Markovian jumping is investigated. In Chapter 8, we conclude the monograph by briefly summarizing the main theoretical findings.

This textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching. It presents the basic principles at an introductory level but emphasizes current advanced level research trends. The material takes into account all the features of Ito equations, Markovian switching, interval systems and time-lag. The theory developed is applicable in different and complicated situations in many branches of science and industry.

This book discusses recent research on the stability of various neural networks with constrained signals. It investigates stability problems for delayed dynamical systems where the main purpose of the research is to reduce the conservativeness of the stability criteria. The book mainly focuses on the qualitative stability analysis of continuous-time as well as discrete-time neural networks with delays by presenting the theoretical development and real-life applications in these research areas. The discussed stability concept is in the sense of Lyapunov, and, naturally, the proof method is based on the Lyapunov stability theory. The present book will serve as a guide to enable the reader in pursuing the study of further topics in greater depth and is a valuable reference for young researcher and scientists.

This book focuses on the stability of the dynamical neural system, synchronization of the coupling neural system and their applications in automation control and electrical engineering. The redefined concept of stability, synchronization and consensus are adopted to provide a better explanation of the complex neural network. Researchers in the fields of dynamical systems, computer science, electrical engineering and mathematics will benefit from the discussions on complex systems. The book will also help readers to better understand the theory behind the control technique and its design.

Nonlinear Stochastic Control and Filtering with Engineering-oriented Complexities presents a series of control and filtering approaches for stochastic systems with traditional and emerging engineering-oriented complexities. The book begins with an overview of the relevant background, motivation, and research problems, and then: Discusses the robust stability and stabilization problems for a class of stochastic time-delay interval systems with nonlinear disturbances Investigates the robust stabilization and H∞ control problems for a class of stochastic time-delay uncertain systems with Markovian switching and nonlinear disturbances Explores the H∞ state estimator and H∞ output feedback controller design issues for stochastic time-delay systems with nonlinear disturbances, sensor nonlinearities, and Markovian jumping parameters Analyzes the H∞ performance for a general class of nonlinear stochastic systems with time delays, where the addressed systems are described by general stochastic functional differential equations Studies the filtering problem for a class of discrete-time stochastic nonlinear time-delay systems with missing measurement and stochastic disturbances Uses gain-scheduling techniques to tackle the probability-dependent control and filtering problems for time-varying nonlinear systems with incomplete information Evaluates the filtering problem for a class of discrete-time stochastic nonlinear networked control systems with multiple random communication delays and random packet losses Examines the filtering problem for a class of nonlinear genetic regulatory networks with state-dependent stochastic disturbances and state delays Considers the H∞ state estimation problem for a class of discrete-time complex networks with probabilistic missing measurements and randomly occurring coupling delays Addresses the H∞ synchronization control problem for a class of dynamical networks with randomly varying nonlinearities Nonlinear Stochastic Control and Filtering with Engineering-oriented Complexities describes novel methodologies that can be applied extensively in lab simulations, field experiments, and real-world engineering practices. Thus, this text provides a valuable reference for researchers and professionals in the signal processing and control engineering communities.