Complex-Valued Neural Networks Systems with Time Delay

ISBN-13: 9789811954528 / Angielski / Miękka / 2023

Ziye Zhang; Zhen Wang;Jian Chen

Opis

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.

Spis treści

Contents

1. Introduction

1.1 Research Significance of Complex-Valued Neural Networks Systems

1.2 History of Complex-Valued Neural Networks Systems

1.3 Book Organization

2. Stability Analysis of Delayed Complex-Valued Neural Networks Systems

2.1 Introduction

2.2 Problem Formulation

2.3 Stability Analysis Based on Separable Method

2.4 Further Stability Analysis Based on Separable Method

2.5 Stability Analysis Based on Nonseparable Method

2.6 Illustrative Examples

2.7 Conclusion and Notes

3. Further Behavior Analysis about Stability and Hopf Bifurcation

3.1 Introduction

3.2 Problem Formulation

3.3 Stability Result

3.4 Hopf Bifurcation Results

3.5 Illustrative Examples

3.6 Conclusion

4. Stability Analysis Based on Nonlinear Measure Approach 

4.1 Introduction

4.2 Problem Formulation

4.3 Sufficient Condition to Ensure the Existence and Uniqueness of the Equilibrium Point

4.4 Finite-Time Stability Result

4.5 Illustrative Examples

4.6 Conclusion

5. Lagrange Exponential Stability for Delayed Complex-Valued Neural Networks Systems 

5.1 Introduction

5.2 Problem Formulation

5.3 Sufficient Criteria Based on Algebraic Structure

5.4 Sufficient Condition in Terms of LMI

5.5 Illustrative Examples

5.6 Conclusion

6. Synchronization Control: Nonseparable Case

6.1 Introduction

6.2 Problem Formulation

6.3 Synchronization Result for Delayed Complex-Valued Inertial Neural Networks 

6.4 Illustrative Example

6.5 Conclusion

7. Anti-Synchronization Control: Nonseparable Case

7.1 Introduction

7.2 Problem Formulation

7.3 Anti-Synchronization Result for Delayed Complex-Valued Inertial Neural Networks

7.4 Anti-Synchronization Result for Delayed Complex-Valued Neural Networks

7.5 Illustrative Examples

7.6 Conclusion

8. Anti-Synchronization Control: Separable Case 

8.1 Introduction

8.2 Problem Formulation

8.3 Anti-Synchronization Result for Delayed Complex-Valued Neural Networks 

8.4 Anti-Synchronization Result for Delayed Complex-Valued Bidirectional Associative Memory Neural Networks

8.5 Illustrative Examples

8.6 Conclusion

9. Finite/Fixed-Time Synchronization Control

9.1 Introduction

9.2 Problem Formulation

9.3 Finite-Time Synchronization Result

9.4 Fixed-Time Synchronization Result

9.5 Illustrative Examples

10. Fixed-Time Pinning Synchronization and Adaptive Synchronization

10.1 Introduction

10.2 Problem Formulation

10.3 Results for Delayed Complex-Valued Inertial Neural Networks 

10.4 Results for Delayed Complex-Valued BAM Neural Networks

10.5 Illustrative Examples

10.6 Conclusion

References

Index

O autorze

Ziye Zhang received the B.Sc. degree in mathematics from Yantai University, Yantai, China, in 2002, the M.Sc. degree in mathematics from Lanzhou University, Lanzhou, China, in 2005, and the Ph.D. degree from the Institute of Complexity Science, Qingdao University, Qingdao, China, in 2015. She is currently Associate Professor with the College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China. Her current research interests include systems analysis, fuzzy control, filter design, and neural networks.

Zhen Wang is currently Professor at College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China. He received Ph.D. degree from School of Automation, Nanjing University of Science and Technology, China, in 2013.

Jian Chen is Associate Professor at School of information and Control Engineering, Qingdao University of Technology, Qingdao, China. She received her Ph.D. degree from Institute of Complexity Science, Qingdao University, in 2017. Her research interest includes systems analysis and control.

Chong Lin is Professor at Institute of Complexity Science, Qingdao University, China. He received Ph.D. from School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, in 1999.