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E-raamat: Qualitative Analysis and Control of Complex Neural Networks with Delays

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Qualitative Analysis and Control of Complex Neural Networks with DelaysSuurem pilt
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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.

Arvustused

Each chapter is independent and self-contained and the book can be read randomly according to one's requirements. This book should benefit researchers and senior graduate/post-graduate students interested in the study of dynamical systems, by providing different kinds of mathematical tools and techniques. this book will definitely benefit readers, providing new insight into the area of neural networks in particular and dynamical systems in general, thereby enriching the literature. (Ponnado Raja Sekhara Rao, Mathematical Reviews, April, 2017)

1 Introduction to Neural Networks
1(36)
1.1 Natural and Artificial Neural Networks
2(1)
1.2 Models of Computation
3(4)
1.3 Networks of Neurons
7(5)
1.4 Associative Memory Networks
12(2)
1.5 Hopfield Neural Networks
14(8)
1.6 Cohen--Grossberg Neural Networks
22(4)
1.7 Property of Neural Network
26(1)
1.8 Information Processing Capacity of Dynamical Systems
27(1)
1.9 Stability of Dynamical Neural Networks
28(2)
1.10 Delay Effects on Dynamical Neural Networks
30(1)
1.11 Features of LMI-Based Stability Results
31(2)
1.12 Summary
33(4)
References
33(4)
2 Preliminaries on Dynamical Systems and Stability Theory
37(54)
2.1 Overview of Dynamical Systems
37(4)
2.2 Definition of Dynamical System and Its Qualitative Analysis
41(3)
2.3 Lyapunov Stability of Dynamical Systems
44(3)
2.4 Stability Theory
47(14)
2.5 Applications of Dynamical Systems Theory
61(2)
2.6 Notations and Discussions on Some Stability Problems
63(22)
2.6.1 Notations and Preliminaries
64(8)
2.6.2 Discussions on Some Stability Definitions
72(13)
2.7 Summary
85(6)
References
86(5)
3 Survey of Dynamics of Cohen--Grossberg-Type RNNs
91(82)
3.1 Introduction
91(4)
3.2 Main Research Directions of Stability of RNNs
95(17)
3.2.1 Development of Neuronal Activation Functions
95(3)
3.2.2 Evolution of Uncertainties in Interconnection Matrix
98(2)
3.2.3 Evolution of Time Delays
100(1)
3.2.4 Relations Between Equilibrium and Activation Functions
101(1)
3.2.5 Different Construction Methods of Lyapunov Functions
102(6)
3.2.6 Expression Forms of Stability Criteria
108(1)
3.2.7 Domain of Attraction
109(1)
3.2.8 Different Kinds of Neural Network Models
110(2)
3.3 Stability Analysis for Cohen--Grossberg-Type RNNs
112(41)
3.3.1 Stability on Hopfield-Type RNNs
112(1)
3.3.2 Stability on Cohen--Grossberg-Type RNNs
113(8)
3.3.3 The Case with Nonnegative Equilibria
121(10)
3.3.4 Stability via M-Matrix or Algebraic Inequality Methods
131(12)
3.3.5 Stability via Matrix Inequalities or Mixed Methods
143(5)
3.3.6 Topics on Robust Stability of RNNs
148(2)
3.3.7 Other Topics on Stability Results of RNNs
150(1)
3.3.8 Qualitative Evaluation on the Stability Results of RNNs
151(2)
3.4 Necessary and Sufficient Conditions for RNNs
153(6)
3.5 Summary
159(14)
References
159(14)
4 Delay-Partitioning-Method Based Stability Results for RNNs
173(32)
4.1 Introduction
173(2)
4.2 Problem Formulation
175(3)
4.3 GAS Criteria with Single Weighting-Delay
178(11)
4.3.1 Weighting-Delay-Independent Stability Criterion
178(6)
4.3.2 Weighting-Delay-Dependent Stability Criterion
184(5)
4.4 GAS Criteria with Multiple Weighting-Delays
189(6)
4.5 Implementation of Optimal Weighting-Delay Parameters
195(1)
4.5.1 The Single Weighting-Delay Case
195(1)
4.5.2 The Multiple Weighting-Delays Case
196(1)
4.6 Illustrative Examples
196(6)
4.7 Summary
202(3)
References
202(3)
5 Stability Criteria for RNNs Based on Secondary Delay Partitioning
205(20)
5.1 Introduction
205(2)
5.2 Problem Formulation and Preliminaries
207(3)
5.3 Global Asymptotical Stability Result
210(10)
5.4 Illustrative Example
220(2)
5.5 Summary
222(3)
References
222(3)
6 LMI-Based Stability Criteria for Static Neural Networks
225(14)
6.1 Introduction
225(1)
6.2 Problem Formulation
226(1)
6.3 Main Results
227(8)
6.4 Illustrative Example
235(1)
6.5 Summary
236(3)
References
236(3)
7 Multiple Stability for Discontinuous RNNs
239(20)
7.1 Introduction
239(2)
7.2 Problem Formulations and Preliminaries
241(2)
7.3 Main Results
243(9)
7.4 Illustrative Examples
252(3)
7.5 Summary
255(4)
References
256(3)
8 LMI-based Passivity Criteria for RNNs with Delays
259(18)
8.1 Introduction
259(2)
8.2 Problem Formulation
261(1)
8.3 Passivity for RNNs Without Uncertainty
262(7)
8.4 Passivity for RNNs with Uncertainty
269(3)
8.5 Illustrative Examples
272(2)
8.6 Summary
274(3)
References
275(2)
9 Dissipativity and Invariant Sets for Neural Networks with Delay
277(34)
9.1 Delay-Dependent Dissipativity Conditions for Delayed RNNs
277(11)
9.1.1 Introduction
277(2)
9.1.2 Problem Formulation
279(2)
9.1.3 θ-dissipativity Result
281(7)
9.2 Positive Invariant Sets and Attractive Sets of DNN
288(12)
9.2.1 Introduction
288(1)
9.2.2 Problem Formulation and Preliminaries
289(2)
9.2.3 Invariant Set Results
291(9)
9.3 Attracting and Invariant Sets of CGNN with Delays
300(7)
9.3.1 Introduction
300(1)
9.3.2 Problem Formulation and Preliminaries
301(3)
9.3.3 Invariant Set Result
304(3)
9.4 Summary
307(4)
References
307(4)
10 Synchronization Stability in Complex Neural Networks
311(22)
10.1 Introduction
311(2)
10.2 Problem Formulation and Preliminaries
313(4)
10.3 Synchronization Results
317(7)
10.4 Illustrative Example
324(5)
10.5 Summary
329(4)
References
329(4)
11 Stabilization of Stochastic RNNs with Stochastic Delays
333(28)
11.1 Introduction
333(2)
11.2 Problem Formulation and Preliminaries
335(4)
11.3 Stabilization Result
339(15)
11.4 Illustrative Examples
354(4)
11.5 Summary
358(3)
References
358(3)
12 Adaptive Synchronization of Complex Neural Networks
361(24)
12.1 Introduction
361(2)
12.2 Problem Formulation and Preliminaries
363(4)
12.3 Adaptive Synchronization Scheme
367(6)
12.4 Illustrative Example
373(6)
12.5 Summary
379(6)
References
380(5)
Index 385
Zhanshan Wang received B.S. degree in Electrical Automation from Inner Mongolia University of Science and Technology, Baotou, China in 1994, M.S. degree in Control Theory and Control Engineering from Liaoning Shihua University, Fushun in 2001 and Ph.D. degree in Control Theory and Control Engineering from Northeastern University, Shenyang in 2006, respectively. From 1994 to 1998 he was a technician in Fushun Plant, Liaoning. He is currently a Professor with the College of Information Science and Engineering, Northeastern University, Shenyang, China. His current research interests include stability analysis of dynamical system, neural networks, complex networks, multi-agent systems, computational intelligence, fault diagnosis, adaptive control and their applications.
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