Boundary Synchronization for Hyperbolic Systems

• Main Authors: Li, Tatsien (Author, http://id.loc.gov/vocabulary/relators/aut), Rao, Bopeng (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Edition: 1st ed. 2019.
• Series: PNLDE Subseries in Control ; 94
• Subjects: System theory.; Partial differential equations.; Differential equations.; Control engineering.; Systems Theory, Control.; Partial Differential Equations.; Ordinary Differential Equations.; Control and Systems Theory.

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 synchronizati...

Table of 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.