Research Directions in Distributed Parameter Systems

, by Smith, Ralph C.; Demetriou, Michael A.

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ISBN: 9780898715484 | 0898715482
Cover: Paperback
Copyright: 11/1/2003

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Research Directions in Distributed Parameter Systems is composed of eleven chapters, written by experts in their respective fields, on topics ranging from control of the Navier-Stokes equations to nondestructive evaluation - all of which are modeled by distributed parameters systems. Written by the plenary speakers for the Conference on Future Directions in Distributed Parameter Systems (October 2000), the volume addresses the state of the art, open questions, and important research directions in applications modeled by partial differential equations and delay systems, with the ultimate goal of passing along these perspectives to researchers in the field.

Foreword

xiii

Preface

xvii

Mathematics and Electromagnetic Theory

(16)

Richard Albanese

Richard Medina

John Penn

Introduction

(1)

Emerging Technologies

(1)

Medical Risk and Electromagnetic Fields

(6)

Biological Effects and Electromagnetism

(4)

Temperature and Tissue Damage

(2)

Effects of Stored Energy

(2)

Applications

(1)

Imaging with Electromagnetic Fields

(1)

Therapy

(1)

Summary and Conclusion

(4)

Bibliography

(3)

Nonlinear Distributed Parameter Control Systems with Non-Normal Linearizations: Applications and Approximations

(38)

John A. Burns

Introduction

(2)

Applications and Approximations

(6)

The Role of Good Applications

(3)

The Role of Approximation

(3)

A Framework for Nonlinear Problems

(13)

Burgers' Equation with Distributed Control

(3)

The General Framework of Ghidaglia and Temam

(2)

Burgers' Equation with Dirichlet Boundary Control

(2)

Burgers' Equation with Neumann Boundary Control

(2)

Control of a Thermal Convection Loop

(4)

Two Model Problems

(6)

Example 1: The Lorenz Equation

(2)

Example 2: A Simple 2n-D Problem

(4)

Conclusions and Suggestions for Future Research

(11)

Bibliography

(9)

Homogenization and Applications to Material Sciences

(40)

Doina Cioranescu

Model Example, Main Homogenization Results

(7)

The Classical Methods in Homogenization

(5)

The Multiple-Scale Method

(2)

Tartar's Oscillating Test Functions Method

(2)

The Two-Scale Convergence

(1)

The Periodic Unfolding Method

(5)

The Periodic Unfolding Operator Tε

(1)

Macro-Micro Decomposition of Functions: The Scale-Splitting Operators Qε and Rε

(2)

Periodic Unfolding and Homogenization

(1)

Corrector Result and Unfolding

(1)

Homogenization in Perforated Domains

(3)

Homogenization of Truss-Like Structures

(10)

The Two-Dimensional Case

(5)

Asymptotic Behavior of Grids

(3)

Asymptotic Behavior of Truss-Like Beams

(1)

Multi-Scale Periodic Unfolding Homogenization

(2)

Homogenization of Rubber-Like Materials

(7)

Bibliography

(2)

Model Reduction for Control Design for Distributed Parameter Systems

(28)

Ruth F. Curtain

Introduction

(4)

Trotter-Kato Semigroup Approximations

(1)

Proper Orthogonal Decomposition Reduced-Order Models

(2)

Approximating via Balanced Truncations

(4)

LQG-Balancing

103

(5)

Numerical Computation of LQG-Balanced Truncations

108

(4)

Robust Controller Design via LQG-Balanced Truncation

112

(4)

Robust Controller Design via LQG-Balanced Truncation

113

(3)

Conclusions

116

(7)

Bibliography

118

(5)

Max-Plus Linear Partial Differential Equations

123

(16)

Wendell H. Fleming

Introduction

123

(1)

Max-Plus Linearity

124

(1)

Time-Dependent HJB Equations

125

(2)

Vanishing Viscosity, Small Random Perturbations

127

(2)

Max-Plus Fundamental Solutions

129

(1)

Max-Plus Probability and Stochastic Calculus

130

(3)

Max-Plus Basis Expansions

133

(1)

Deterministic Nonlinear Filtering

134

(5)

Bibliography

135

(4)

Geometric Theory of Output Regulation for Linear Distributed Parameter Systems

139

(30)

C. I. Byrnes

D. S. Gilliam

V. I. Shubov

Introduction

140

(2)

Bounded Input-Output

142

(2)

The Regulator Equations and Proof of the Main Theorem

144

(6)

Unbounded Inputs and Outputs

150

(2)

Examples of Regular Linear Systems

152

(3)

Systems with Delays

155

(5)

Tracking and Disturbance Rejection for an Oscillator with Delayed Damping

160

(2)

Future Directions

162

(7)

Bibliography

165

(4)

Smart Structures, Structural Health Monitoring and Crack Detection

169

(18)

Daniel J. Inman

Sergio H. S. Carneiro

Smart Materials and Structures

169

(1)

Structural Health Monitoring

170

(4)

Vibration Suppression

174

(3)

Simultaneous Diagnostics and Control (Level 7)

177

(2)

Self-Healing (Level 6)

179

(1)

Diagnostics of Cracked Beams via Genetic Algorithms (Level 3)

179

(3)

Future Directions

182

(2)

Summary

184

(3)

Bibliography

185

(2)

Survey of Research in Modeling the Human Respiratory and Cardiovascular Systems

187

(32)

F. Kappel

J. J. Batzel

Respiratory System Modeling

188

(6)

Introduction

188

(1)

Survey of Modeling Developments

189

(5)

Current Issues

194

(1)

Models of the Cardiovascular System

194

(7)

Introduction

194

(3)

Survey of Modeling Efforts

197

(3)

Current Issues

200

(1)

Combined Cardiovascular-Respiratory Models

201

(18)

Introduction

201

(2)

A Cardiovascular-Respiratory Model Application

203

(1)

Current Issues

204

(1)

Appendix

205

(1)

Respiratory Model Proposed by Khoo et al

205

(2)

Cardiovascular-Respiratory Model Proposed by Timischl and Kappel 1998

207

(4)

Bibliography

211

(8)

Inverse Problems Related to Electromagnetic Nondestructive Evaluation

219

(18)

Fumio Kojima

Introduction

219

(2)

Parameter Estimation Arising in ECT

221

(6)

Mathematical Model for Inspection Procedures

221

(3)

Mathematical Description of the Observation Mechanism

224

(1)

Inverse Problems and the Associated Parameter Estimation

224

(3)

Inverse Problems for Natural Crack

227

(2)

JSAEM Benchmark Problems

227

(1)

Inverse Analysis by Evolutionary Computation

227

(2)

Open Problems and Current Research Directions

229

(1)

Nondestructive Evaluation of Material Degradation

229

(4)

Characterization of B-H Curve

230

(1)

Stochastic Analysis of the Barkhausen Effect

231

(1)

Structure-Sensitive Magnetic Characterization by Nano-Scale Flaws

232

(1)

Concluding Remarks

233

(4)

Bibliography

233

(4)

Some Suboptimal Strategies for Numerical Realization of Large-Scale Optimal Control Problems

237

(20)

Karl Kunisch

Introduction

237

(1)

A Model Problem

238

(3)

Instantaneous Control-Receding Horizon Control

241

(5)

Reduced-Order Methods

246

(5)

Comments on Suboptimal Closed-Loop Methods

251

(2)

Conclusions

253

(4)

Bibliography

254

(3)

Results and Conjectures for the Control of Navier--Stokes Equations

257

(12)

J. L. Lions

Introduction

258

(2)

The First Two Conjectures Relative to Approximate Controllability

260

(2)

Sensitivity to Reynolds Number

262

(1)

An Attempt to Nonlinear Duality

263

(3)

Further Remarks

266

(3)

Bibliography

267

(2)

Index

269

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Research Directions in Distributed Parameter Systems

Summary

Table of Contents

Supplemental Materials