1st Edition
Modeling and Control in Vibrational and Structural Dynamics A Differential Geometric Approach
Preliminaries from Differential Geometry
Linear Connections, Differential of Tensor Fields, and Curvature
Distance Functions
A Basic Computational Technique
Sobolev Spaces of Tensor Field and Some Basic Differential Operators
Control of the Wave Equation with Variable Coefficients in Space
How to Understand Riemannian Geometry as a Necessary Tool for Control of the Wave Equation with Variable Coefficients
Geometric Multiplier Identities
Escape Vector Fields and Escape Regions for Metrics
Exact Controllability. Dirichlet/Neumann Action
Smooth Controls
A Counterexample without Exact Controllability
Stabilization
Transmission Stabilization
Control of the Plate with Variable Coefficients in Space
Multiplier Identities
Escape Vector Fields for the Plate
Exact Controllability from Boundary
Controllability for Transmission of Plate
Stabilization from Boundary for the Plate with a Curved Middle Surface
Linear Shallow Shells: Modeling and Control
Equations in Equilibrium. Green’s Formulas
Ellipticity of the Strain Energy of Shallow Shells
Equations of Motion
Multiplier Identities
Escape Vector Field and Escape Region for the Shallow Shell
Observability Inequalities. Exact Controllability
Exact Controllability for Transmission
Stabilization by Linear Boundary Feedbacks
Stabilization by Nonlinear Boundary Feedbacks
Naghdi’s Shells: Modeling and Control
Equations of Equilibrium. Green’s Formulas. Ellipticity of the Strain Energy. Equations of Motion
Observability Estimates from Boundary
Stabilization by Boundary Feedback
Stabilization of Transmission
Koiter’s Shells: Modeling and Controllability
Equations of Equilibria. Equations of Motion
Uniqueness for the Koiter Shell
Multiplier Identities
Observability Estimates from Boundary
Control of the Quasilinear Wave Equation in Higher Dimensions
Boundary Traces and Energy Estimates
Locally and Globally Boundary Exact Controllability
Boundary Feedback Stabilization
Structure of Control Regions for Internal Feedbacks
References
Bibliography
Index
Notes and References appear at the end of each chapter.
Biography
Peng-Fei Yao is a professor in the Key Laboratory of Systems and Control in the Chinese Academy of Sciences. His research interests include control and modeling of vibrational mechanics, the scattering problem of vibrational systems, global and blow-up solutions, and nonlinear elasticity.
