Franklin

Boundary Synchronization for Hyperbolic Systems / by Tatsien Li, Bopeng Rao.

Author/Creator:
Li, Daqian author., Author,
Edition:
1st ed. 2019.
Publication:
Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
Series:
Mathematics and Statistics (Springer-11649)
PNLDE Subseries in Control ; 94
PNLDE Subseries in Control ; 94
Format/Description:
Book
1 online resource (X, 333 pages) : 2 illustrations, 1 illustrations in color.
Subjects:
System theory.
Differential equations, Partial.
Differential equations.
Automatic control.
Local subjects:
Systems Theory, Control. (search)
Partial Differential Equations. (search)
Ordinary Differential Equations. (search)
Control and Systems Theory. (search)
System Details:
text file PDF
Summary:
Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs). By combining synchronization with controllability, they introduce the study of synchronization to the field of control and add new perspectives to the investigation of synchronization for systems of PDEs. With a focus on synchronization for a coupled system of wave equations, the text is divided into three parts corresponding to Dirichlet, Neumann, and coupled Robin boundary controls. Each part is then subdivided into chapters detailing exact boundary synchronization and approximate boundary synchronization, respectively. The core intention is to give artificial intervention to the evolution of state variables through appropriate boundary controls for realizing the synchronization in a finite time, creating a novel viewpoint into the investigation of synchronization for systems of partial differential equations, and revealing some essentially dissimilar characteristics from systems of ordinary differential equations. Primarily aimed at researchers and graduate students of applied mathematics and applied sciences, this text will particularly appeal to those interested in applied PDEs and control theory for distributed parameter systems.
Contents:
Introduction and Overview
Preliminaries
Part 1: Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Exact Boundary Synchronization
Exact boundary controllability and non-exact boundary controllability
Exact boundary synchronization and non-exact boundary synchronization
Exactly synchronizable states
Exact boundary synchronization by groups
Exactly synchronizable states by p-groups
Part 2: Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Approximate Boundary Synchronization
Approximate boundary synchronization
Approximate boundary synchronization by p-groups
Induced approximate boundary synchronization
Part 3: Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Exact Boundary Synchronization
Exact boundary controllability and non-exact boundary controllability
Exact boundary synchronization and non-exactly boundary synchronization
Exact boundary synchronization by p-groups
Determination of exactly synchronizable states by p-groups
Part 4: Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Approximate Boundary Synchronization
Approximate boundary null controllability
Approximate boundary synchronization
Approximate Boundary Synchronization by p-groups
Part 5: Synchronization for a Coupled System of Wave Equations with Coupled Robin Boundary Controls: Exact Boundary Synchronization
Preliminaries on problem (III) and (III0)
Exact boundary controllability and non-exact boundary controllability
Exact boundary synchronization
Determination of exactly synchronizable states
Exact boundary synchronization by p-groups
Necessity of the conditions of Cp-compatibility
Determination of exactly synchronizable states by p-groups
Part 6. Synchronization for a Coupled System of Wave Equations with Coupled Boundary Controls: Approximate Boundary Synchronization
Some algebraic lemmas
Approximate boundary null controllability
Unique continuation for Robin problem
Approximate boundary synchronization
Approximate boundary synchronization by p-groups
Approximately synchronizable states by p-groups
Closing remarks.
Contributor:
Rao, Bopeng. author., Author,
SpringerLink (Online service)
Contained In:
Springer eBooks
Other format:
Printed edition:
Printed edition:
Printed edition:
ISBN:
978-3-030-32849-8
9783030328498
Publisher Number:
10.1007/978-3-030-32849-8 doi
Access Restriction:
Restricted for use by site license.
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