Synchronization for Wave Equations with Locally Distributed Controls / by Tatsien Li, Bopeng Rao.

Format:

Book

Author/Creator:

Li, Daqian.

Contributor:

Rao, Bopeng.

Series:

Series in Contemporary Mathematics, 2364-0103 ; 5

Language:

English

Subjects (All):

System theory.

Control theory.

Differential equations.

Functional analysis.

Systems Theory, Control.

Differential Equations.

Functional Analysis.

Local Subjects:

Systems Theory, Control.

Differential Equations.

Functional Analysis.

Physical Description:

1 online resource (199 pages)

Edition:

1st ed. 2024.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2024.

Summary:

This book aims to establish a systematic theory on the synchronization for wave equations with locally distributed controls. It is structured in two parts. Part I is devoted to internal controls, while Part II treats the case of mixed internal and boundary controls. The authors present necessary mathematical formulations and techniques for analyzing and solving problems in this area. They also give numerous examples and applications to illustrate the concepts and demonstrate their practical relevance. The book provides an overview of the field and offers an in-depth analysis of new results with elegant proofs. By reading this book, it can be found that due to the use of internal controls, more deep-going results on synchronization can be obtained, which makes the corresponding synchronization theory more precise and complete. Graduate students and researchers in control and synchronization for partial differential equations, functional analysis find this book useful. It is also an excellent reference in the field. Thanks to the explicit criteria given in this book for various notions of controllability and synchronization, researchers and practitioners can effectively use the control strategies described in this book and make corresponding decisions regarding system design and operation.

Contents:

1. Introduction

2. Algebraic preliminaries

3. Approximate internal controllability

4. Indirect internal controls

5. Approximate internal synchronization

6. Approximate internal synchronization by groups

7. Exact internal controllability

8. Exact internal synchronization

9. Stability of exact internal synchronization

10. Exact internal synchronization by groups

11. Stability of exact internal synchronization by groups

12. Family of exact internal synchronizations

13. Approximate mixed controllability

14. Approximate mixed synchronization by groups

15. Exact mixed controllability

16. Exact mixed synchronization by groups.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

981-9709-92-X

OCLC:

1436830826