<p><p>This book describes a model-based development approach for globally-asynchronous locally-synchronous distributed embedded controllers. This approach uses Petri nets as modeling formalism to create platform and network independent models supporting the use of design automation tools. To support
Synchronization for Wave Equations with Locally Distributed Controls
β Scribed by Tatsien Li, Bopeng Rao
- Publisher
- Springer
- Year
- 2024
- Tongue
- English
- Leaves
- 199
- Series
- Series in Contemporary Mathematics
- Category
- Library
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
β¦ Table of Contents
Preface
Contents
1 Introduction
References
2 Algebraic Preliminaries
References
Part I System ofΒ Wave Equations withΒ Internal Controls
3 Approximate Internal Controllability
3.1 Internal D-observability
3.2 A Uniqueness Theorem
3.3 Approximate Internal Controllability
References
4 Indirect Internal Controls
4.1 An Algebraic Procedure of Reduction
4.2 Mathematical Analysis
4.3 Indirect Internal Controls
References
5 Approximate Internal Synchronization
5.1 Introduction
5.2 Approximate Internal Synchronization
5.3 Condition of C1-Compatibility
5.4 Internal Pinning Synchronization
References
6 Approximate Internal Synchronization by Groups
6.1 Approximate Internal Synchronization by Groups
6.2 Condition of Cp-Compatibility
6.3 Induced Internal Synchronization
6.4 Stability of Approximate Internal Synchronization by Groups
6.5 Stability of Approximate Internal Synchronization by Groups (Continued)
6.6 Internal Pinning Synchronization by Groups
References
7 Exact Internal Controllability
7.1 Introduction
7.2 Exact Internal Controllability
7.2.1 Exact Internal Controllability
7.2.2 Proof of Theorem 7.2
7.3 Non Exact Internal Controllability
7.4 Approximate Internal Controllability (Continued)
References
8 Exact Internal Synchronization
8.1 Exact Internal Synchronization
8.2 Exactly Synchronizable State
9 Stability of Exact Internal Synchronization
9.1 Pre-synchronized State
9.2 Attainable Set of Exact Internal Synchronization
9.3 Stability of Exact Internal Synchronization
References
10 Exact Internal Synchronization by Groups
10.1 Exact Internal Synchronization by Groups
10.2 Exactly Synchronizable State by Groups
Reference
11 Stability of Exact Internal Synchronization by Groups
11.1 Pre-synchronized State by Groups
11.2 Attainable Set of Exact Internal Synchronization by Groups
11.3 Stability of Exact Internal Synchronization by Groups
11.4 Comments
References
12 Family of Exact Internal Synchronizations
12.1 Generalized Synchronization
12.2 Family of Exact Internal Synchronizations
References
Part II System ofΒ Wave Equations withΒ Mixed Internal andΒ Boundary Controls
13 Approximate Mixed Controllability
13.1 Introduction
13.2 A Uniqueness Theorem
13.3 Approximate Mixed Controllability
References
14 Approximate Mixed Synchronization by Groups
14.1 Approximate Mixed Synchronization by Groups
14.2 Approximate Mixed Synchronization by Groups (Continued)
14.3 Condition of Cp-compatibility
14.4 Induced Mixed Synchronization
14.5 Stability of Approximate Mixed Synchronization by Groups
14.6 Mixed Pinning Synchronization
References
15 Exact Mixed Controllability
15.1 Exact Mixed Controllability
15.2 Non Exact Mixed Controllability
References
16 Exact Mixed Synchronization by Groups
16.1 Exact Mixed Synchronization by Groups
16.2 Condition of Cp-compatibility
16.3 Attainable Set of the Exact Mixed Synchronization by Groups
16.4 Stability of Exact Mixed Synchronization by Groups
References
Index
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