Amouroux / El Jai Control of Distributed Parameter Systems 1989

Selected Papers from the 5th IFAC Symposium, Perpignan, France, 26-29 June 1989
1. Auflage 2014
ISBN: 978-1-4832-9881-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 523 Seiten, Web PDF

Reihe: IFAC Symposia Series

This volume presents state-of-the-art reports on the theory, and current and future applications of control of distributed parameter systems. The papers cover the progress not only in traditional methodology and pure research in control theory, but also the rapid growth of its importance for different applications. This title will be of interest to researchers working in the areas of mathematics, automatic control, computer science and engineering.

Autoren/Hrsg.

Amouroux, M.

El Jai, A.

Inhaltsverzeichnis

1;Front Cover;1
2;Control of Distributed Parameter Systems 1989;4
3;Copyright Page;5
4;Table of Contents;10
5;PLENARY SESSIONS;10
6;FOREWORD;8
7;PART 1: PLENARY SESSIONS;18
7.1;Chapter 1. Sentinels with Special Sensitivity;18
7.1.1;1. Introduction;18
7.1.2;2. Sentinels;18
7.1.3;3. Analytic formulation of the problem.;19
7.1.4;4. Reduction to a new type of exact controllability problem.;19
7.1.5;5. Penalization.;20
7.1.6;6. Optimality system (formal).;20
7.1.7;7. Operator . and new functional space.;20
7.1.8;References.;21
7.2;Chapter 2. Linear Quadratic Tracking Problems in Hubert Space: Application to Optimal

Active Noise Suppression;22
7.2.1;1 Introduction;22
7.2.2;2 Finite time interval problem;22
7.2.3;3 Infinite time interval problem;23
7.2.4;4 Finite dimensional approximation;25
7.2.5;5 Examples and concluding remarks;26
7.2.6;6 Acknowledgements;27
7.2.7;References;27
7.3;Chaptyer 3. Some Results on Exact Controllability;28
7.3.1;Introduction;28
7.3.2;1. A general framework;28
7.3.3;2. Dynamic Systems. Controllability Operator;30
7.3.4;3. Controllability for the wave equation with Dirichlet conditions;31
7.3.5;REFERENCES;32
7.4;Chapter 4. Time and Frequency Domain Methods for Infinite-dimensional H -control;34
7.4.1;1. INTRODUCTION;34
7.4.2;2. THE CALLIER-DESOER CLASS OF TRANSFER FUNCTIONS;34
7.4.3;3. THE PRITCHARD-SALAMON CLASS OF STATE-SPACE SYSTEMS;35
7.4.4;4. H°°-CONTROL THEORY FOR THE PRITCHARD-SALAMON CLASS;37
7.4.5;CONCLUSIONS;37
7.4.6;REFERENCES;37
7.5;Chapter 5. Compensator Design for Stability Enhancement with Co-located Controllers;40
7.5.1;1. INTRODUCTION;40
7.5.2;2. A CONCRETE MODEL;40
7.5.3;3. THE ABSTRACT MODEL;41
7.5.4;4. COMPENSATOR DESIGN;43
7.5.5;5. COMPENSATOR TRANSFER FUNCTION;45
7.5.6;6. PERFORMANCE EVALUATION;46
7.5.7;REFERENCES;48
7.6;Chapter 6. Shape Analysis and Optimization in Distributed Parameter Systems;52
7.6.1;1. INTRODUCTION.1;52
7.6.2;2. EXAMPLES OF SHAPE OPTIMIZATION PROBLEMS.;53
7.6.3;3. SHAPE SENSITIVITY ANALYSIS.;54
7.6.4;4. SHAPE IDENTIFICATION PROBLEMS.;56
7.6.5;5. SHAPE CONTROL PROBLEMS.;57
7.6.6;6. EXISTENCE OF OPTIMAL SHAPES.;57
7.6.7;REFERENCES;58
8;PART 2: SYSTEM ANALYSIS;62
8.1;Chapter 1. Controllability of Damped Flexible Systems;62
8.1.1;INTRODUCTION;62
8.1.2;1. HUN WITH SEMIGROUP APPROACH;62
8.1.3;2. CONTROLLABILITY OF WEAKLY DAMPED FLEXIBLE SYSTEMS;63
8.1.4;3. CONTROLLABILITY OF STRONGLY DAMPED FLEXIBLE SYSTEMS;64
8.1.5;REFERENCES;66
8.2;Chapter 2. Stabilization of Second Order Evolution Equations by Unbounded Nonlinear Feedback;68
8.2.1;INTRODUCTION;68
8.2.2;THE MAIN RESULT;69
8.2.3;APPLICATION;69
8.2.4;PROOF OF THEOREM 1;70
8.2.5;A PARTIAL CONVERSE TO THEOREM 1;72
8.2.6;REFERENCES;73
8.3;Chapter 3. Stability of Perturbed Linear Distributed Parameter Systems: A Lyapunov

Equation Approach;74
8.3.1;1. Introduction;74
8.3.2;2. The nominal system and its perturbations;74
8.3.3;3. Perturbations of the Lyapunov Equation;75
8.3.4;REFERENCES;79
8.4;Chapter 4. Stabilizability of Distributed Parameter Systems with Unbounded Controls;80
8.4.1;0. Introduction;80
8.4.2;1. Example;82
8.4.3;3. Systems for which (NC) are necessary conditions for stabil izability;83
8.4.4;Conclusions;85
8.4.5;References;85
8.5;Chapter 5. Weak Asymptotic Stability for Discrete Linear Distributed Systems;86
8.5.1;1. NOTATION AND TERMINOLOGY;86
8.5.2;2. INTRODUCTION;86
8.5.3;3. WEAKLY CONVERGENT POWER SEQUENCES;87
8.5.4;4. WEAK ASYMPTOTIC STABILITY;88
8.5.5;5. CONCLUDING REMARKS;89
8.5.6;REFERENCES;90
8.6;Chapter 6. Time-domain Feedback Control of Distributed Parameter Systems Using

Approximate Models - An Operational Approach;92
8.6.1;INTRODUCTION;92
8.6.2;THE GENERALIZED SIGNALS;92
8.6.3;THE GENERALIZED PLANTS;92
8.6.4;RESULTS;93
8.6.5;IN APPLICATION;93
8.6.6;SUMMARY;94
8.6.7;REFERENCES;94
8.7;Chapter 7. Exact Controllability and Optimal Control of Distributed Systems;96
8.7.1;INTRODUCTION;96
8.7.2;I- EXACT CONTROLLABILITY;96
8.7.3;II- CONTROL PROBLEM ;99
8.7.4;CONCLUSION :;101
8.7.5;REFERENCES;101
8.8;Chapter 8. On Some Mathematical Tools for Local Controllability;102
8.8.1;INTRODUCTION;102
8.8.2;OPEN MAPPING RESULTS;103
8.8.3;REFERENCES;105
8.9;Chapter 9. The Edge Theorem and Graphical Tests for Robust Stability of Neutral

Time-delay Systems;106
8.9.1;1 Introduction;106
8.9.2;2 Problem Formulation and Notation;107
8.9.3;3 D-Stability Criteria for a Polytope of Neutral Time-Delay Systems;108
8.9.4;4 A Graphical Approach for Checking Ins tability of Neutral Time-Delay Systems;108
8.9.5;5 Conclusion;109
8.9.6;References;109
8.10;Chapter 10. Remarks on the Homogenization and Boundary Control of Distributed Systems;110
8.10.1;I. Introduction;110
8.10.2;II. Two control problems We consider the one-parameter family of elliptic operators;110
8.10.3;III. Solution of the stationary problem;111
8.10.4;IV. Exact Controllability;111
8.10.5;V. Concluding Remarks;112
8.10.6;References;112
8.11;Chapter 11. On Hubert Uniqueness Method: A Semigroup Approach;114
8.11.1;INTRODUCTION;114
8.11.2;1. HUM BY SEMIGROUP APPROACH;114
8.11.3;2. GENERALIZATION OF HUN;115
8.11.4;Conclusion;119
8.11.5;REFERENCES;119
8.12;Chapter 12. Stability and Structural Properties of Infinite Dimensional Balanced Realizations;120
8.12.1;1 Introduction;120
8.12.2;2 Discrete time balanced realizations;120
8.12.3;3 Continuous time balanced realizations;121
8.12.4;4 Connection between continuous and discrete time systems;122
8.12.5;5 Output normal realizations;123
8.12.6;6 Sign symmetry and stability of balanced realizations;124
8.12.7;References;126
8.13;Chapter 13. Open Loop Stabilizability, A Research Note;128
8.13.1;1. INTRODUCTION.;128
8.13.2;2. CLOSED-LOOP STABILIZABILITY.;128
8.13.3;3. OPEN LOOP STABILIZABILITY.;129
8.13.4;4- THE RELATION BETWEEN OPEN AND CLOSED LOOP STABILIZABILITY;129
8.13.5;REFERENCES;132
8.14;Chapter 14. Robustness Optimization for Abstract, Uncertain Control Systems: Unbounded Inputs and Perturbations;134
8.14.1;§0 Introduction;134
8.14.2;§2StabiIity radius optimisation and SIARE;136
8.14.3;§3 References;138
9;PART 3: APPLICATIONS;140
9.1;Chapter 1. On-line Parameter Identification of the Rhine River Calamity Model;140
9.1.1;INTRODUCTION;140
9.1.2;APPROXIMATE ANALYTICAL SOLUTION;140
9.1.3;IDENTIFICATION ALGORITHM;142
9.1.4;SIMULATIONAL AND REAL-TIME EXPERIMENTS;142
9.1.5;CONCLUSIONS;143
9.1.6;REFERENCES;143
9.2;Chapter 2. Control of Distributed Parameter Bioreactors Via Orthogonal Collocation;146
9.2.1;1. INTRODUCTION;146
9.2.2;2. DYNAMICAL MODEL OF FLUIDIZED AND PACKED BED BIOREACTORS;147
9.2.3;3. REDUCTION OF THE DISTRIBUTED PARAMETER MODEL TO ORDINARY DIFFERENTIAL EQUATIONS;147
9.2.4;4. THE CONTROL ALGORITHM;148
9.2.5;5. CONCLUSIONS;150
9.2.6;A cknowledgement;150
9.2.7;REFERENCES;150
9.3;Chapter 3. Parameter Estimation in Stochastic Hydraulic Models;152
9.3.1;INTRODUCTION;152
9.3.2;THE DYNAMICAL MODEL;152
9.3.3;NUMERICAL REPRESENTATION;153
9.3.4;THE ESTIMATION ALGORITHM;153
9.3.5;RESULTS;155
9.3.6;DISCUSSION;155
9.3.7;REFERENCES;156
9.4;Chapter 4. Optimal Control of a Non-linear System;158
9.4.1;1 Introduction;158
9.4.2;2 Equations of the model;158
9.4.3;3 Numerical solution of the system;159
9.4.4;4 Optimal boundary control;159
9.4.5;5 Numerical results - Conclusions;161
9.4.6;References;162
9.5;Chapter 5. Pareto Optimal Birth Control of Age-dependent Populations;164
9.5.1;INTRODUCTION;164
9.5.2;DUBOVITSKII-MILYUTIN THEOREM (Girsonov, 1972);165
9.5.3;PROBLEM WITH N0NSM00TH CRITERIA;166
9.5.4;REFERENCES;168
9.6;Chapter 6. Optimal Control of a Nonlinear Thermal System;170
9.6.1;INTRODUCTION;170
9.6.2;PRELIMINARY RESULTS;170
9.6.3;DISCRETE CONTROL PROBLEM;171
9.6.4;NUMERICAL RESULTS;174
9.6.5;REFERENCES;175
9.7;Chapter 7. Identification of the Plasma Current Density in a Tokamak;176
9.7.1;INTRODUCTION;176
9.7.2;THE PHYSICAL MODEL;176
9.7.3;THE INVERSE PROBLEM;177
9.7.4;NUMERICAL RESOLUTION;178
9.7.5;PHYSICAL RESULTS;178
9.7.6;REFERENCES;178
10;PART 4: PARAMETER ESTIMATION IN DPS;182
10.1;Chapter 1. Two-dimensional Inverse Scattering Methods in Ultrasound Computer Tomography;182
10.1.1;INTRODUCTION;182
10.1.2;THE EIKONAL APPROXIMATION;182
10.1.3;SCANNING GEOMETRIES IN TWO DIMENSIONS;183
10.1.4;LIMITED APERTURE;184
10.1.5;REFERENCES;184
10.2;Chapter 2. A Numerical Method for Parameter Estimation in Moving Boundary Problems;186
10.2.1;INTRODUCTION;186
10.2.2;MODEL EQUATIONS: STEFAN PROBLEM;186
10.2.3;DYNAMIC ALGORITHM;187
10.2.4;FREE ALGORITHM;188
10.2.5;NUMERICAL INVESTIGATIONS;188
10.2.6;CONCLUSIONS;189
10.2.7;REFERENCES;190
10.3;Chapter 3. Determining the Nonlinearity in a Parabolic Equation from Boundary Measurements;198
10.3.1;Introduction;198
10.3.2;Strategy for uniqueness;199
10.3.3;Semigroup formulation;199
10.3.4;Construction; Verification of hypotheses;199
10.3.5;Uniqueness;201
10.3.6;Appr oximat ion;202
10.3.7;Summary;203
10.3.8;ACKNOWLEDGMENT;203
10.3.9;REFERENCES;203
10.4;Chapter 4. A Computational Method for Electrical Impedance Imaging;204
10.4.1;INTRODUCTION;204
10.4.2;BACKPROJECTION AND RADON TRANSFORM;204
10.4.3;NUMERICAL IMPLEMENTATION AND ITERATIVE REFINEMENT;206
10.4.4;LINEARIZED INVERSE PROBLEM FOR A POLYGONAL DOMAIN;208
10.4.5;CONCLUSION;209
10.4.6;REFERENCES;209
10.5;Chapter 5. Multiscale Parametrization for the Estimation of a Diffusion Coefficient in Elliptic and Parabolic Problems;210
10.5.1;1-INTRODUCTION;210
10.5.2;2-THE PARAMETER ESTIMATION PROBLEMS UNDER CONSIDERATION;210
10.5.3;3-DEFINITION OF LOCAL AND MULTISCALE BASIS;211
10.5.4;4-LOCAL VERSUS MULTISCALE BASIS I: VELOCITY, HESSIAN, RADII OF CURVATURE;212
10.5.5;5-LOCAL VERSUS MULTISCALE BASIS . :

OPTIMIZATION RUNS;213
10.5.6;6-IMPLEMENTATION;214
10.5.7;7-CONCLUSIONS;214
10.5.8;8-REFERENCES;214
10.6;Chapter 6. Multiscale Parametrization for the Estimation of a Diffusion Coefficient in Elliptic and Parabolic Problems;210
10.6.1;1-INTRODUCTION;210
10.6.2;2-THE PARAMETER ESTIMATION PROBLEMS UNDER CONSIDERATION;210
10.6.3;3-DEFINITION OF LOCAL AND MULTISCALE BASIS;211
10.6.4;4-LOCAL VERSUS MULTISCALE BASIS I: VELOCITY, HESSIAN, RADII OF CURVATURE;212
10.6.5;5-LOCAL VERSUS MULTISCALE BASISII : OPTIMIZATION RUNS;213
10.6.6;6-IMPLEMENTATION;214
10.6.7;7-CONCLUSIONS;214
10.6.8;8-REFERENCES;214
10.7;Chapter 7. Error Estimation for Determination of Unknown Coefficients in Parabolic Equations;220
10.7.1;INTRODUCTION;220
10.7.2;A MARCHING METHOD IN SPACE WITH HYPERBOLIC PERTURBATION;221
10.7.3;PROOF OF THEOREM 2;223
10.7.4;REFERENCES;224
10.8;Chapter 8. On-line Identification of the State of the Surface of a Material Undergoing Thermal Processing;226
10.8.1;INTRODUCTION;226
10.8.2;PRESENTATION OF THE METHOD;227
10.8.3;RESULTS AND DISCUSSION;228
10.8.4;CONCLUSION;230
10.8.5;ACKNOWLEDGEMENT;230
10.8.6;REFERENCES;230
11;PART 5: MOVING DOMAIN AND SHAPE OPTIMISATION;232
11.1;Chapter 1. Computation of the Shape Hessian by a Lagrangian Method;232
11.1.1;1. INTRODUCTION.1;232
11.1.2;2. DEFINITIONS AND STRUCTURE THEOREMS.;232
11.1.3;3. SHAPE GRADIENT VIA DIFFERENTIABILITY OF A SADDLE POINT.;234
11.1.4;4. SHAPE HESSIAN VIA DIFFERENTIABILITY OF A SADDLE POINT.;234
11.1.5;REFERENCES;237
11.2;Chapter 2. Shape Acceleration: A Second Order Accurate Incremental Method for Big Deformations;238
11.2.1;INTRODUCTION;238
11.2.2;QUASISTEADY VISCOPLASTIC FLOW;238
11.2.3;SHAPE ACCELERATION;239
11.2.4;FINITE ELEMENT MODEL;240
11.2.5;NUMERICAL EXPERIMENTS;240
11.2.6;REFERENCES;240
11.3;Chapter 3. On Shape Sensitivity Analysis for Visco-Elastic-Plastic Problems;242
11.3.1;ABSTRACT PROBLEM;242
11.3.2;VISCO-ELASTIC-PLASTIC PROBLEM;243
11.3.3;APPENDIX A;245
11.3.4;REFERENCES;245
11.4;Chapter 4. Dynamical Actuators for the Heat Equation;246
11.4.1;1. INTRODUCTION;246
11.4.2;2. DYNAMICAL ACTUATORS;246
11.4.3;3. EXISTENCE AND UNIQUENESS OF SOLUTIONS TO HAMILTON-JACOBI EQUATIONS;248
11.4.4;4. CONCLUSION;249
11.4.5;REFERENCES;249
11.5;Chapter 5. Static Shape Estimation and Failure Detection in Large Spaceborne Antennas Via Computer Vision;250
11.5.1;1. INTRODUCTION;250
11.5.2;2. STATEMENT OF SHAPE ESTIMATION PROBLEM;250
11.5.3;3. GEOMETRIC RELATIONS;251
11.5.4;4. HUB ATTITUDE ESTIMATION;251
11.5.5;5. RIB SHAPE ESTIMATION;252
11.5.6;6. DETECTION OF FAILURE AND ABNORMAL CONDITIONS;253
11.5.7;7. EXPERIMENTAL STUDY;254
11.5.8;8. DISCUSSION AND CONCLUDING REMARKS;254
11.5.9;REFERENCES;254
11.6;Chapter 6. Relaxation Methods for the Study of Domain Optimization Problems;258
11.6.1;INTRODUCTION;258
11.6.2;A FREE BOUNDARY VALUE PROBLEM;258
11.6.3;REFERENCES;260
11.7;Chapter 7. Stabilization of Wave Equation by Periodical Moving Actuators;262
11.7.1;Introduction;262
11.7.2;Existence result;263
11.7.3;Theorem;263
11.7.4;Proof of thetheorem;263
11.7.5;Remark;264
11.7.6;References;264
12;PART 6: ALGORITHMIC ASPECTS IN PARAMETER ESTIMATION;266
12.1;Chapter 1. Shape Identification Technique for a 2-D Elliptic System by Boundary Integral Equation Method;266
12.1.1;INTRODUCTION;266
12.1.2;EXISTENCE OF SOLUTIONS;267
12.1.3;INTEGRAL EQUATION MODEL AND ITS NUMERICAL SCHEMES;267
12.1.4;COMPUTATIONAL METHOD FOR DOMAIN IDENTIFICATION;268
12.1.5;NUMERICAL EXPERIMENTS;270
12.1.6;ACKNOWLEDGEMENT;271
12.1.7;REFERENCES;271
12.2;Chapter 2. Gradpack: A Symbolic System for Automatic Generation of Numerical Programs in Parameter Estimation;272
12.2.1;INTRODUCTION;272
12.2.2;TRANSLATOR;273
12.2.3;EXTENSION OF DIFFERENTIAL CALCULUS;273
12.2.4;MODEL;274
12.2.5;SOLUTION OF EQUATION AND CALCULATION OF GRADIENT WITH AJOINT EQUATION;274
12.2.6;CONCLUSIONS;275
12.2.7;REFERENCES;275
12.3;Chapter 3. Sequential Quadratic Programming for Parameter Identification Problems;276
12.3.1;INTRODUCTION;276
12.3.2;VERIFACATION OF NONDEGENERACY;278
12.3.3;PROBLEM REDUCTION;279
12.3.4;SUFFICIENT CONDITIONS;279
12.3.5;CONCLUSIONS;280
12.3.6;A CKNO WLEDGEMENTS;280
12.3.7;REFERENCES;280
13;PART 7: OPTIMAL CONTROL;282
13.1;Chapter 1. The LQCP with a Terminal Inequality Constraint and Unbounded Input and Output Operators;282
13.1.1;INTRODUCTION;282
13.1.2;STATEMENT OF THE PROBLEM;282
13.1.3;AUXILIARY RESULTS;283
13.1.4;RELATIONSHIP BETWEEN (P-A) AND THE MINIMUM ENERGY PROBLEM;283
13.1.5;SOLUTION OF THE PROBLEM (A);284
13.1.6;SOLUTION OF THE PROBLEM (P-A);285
13.1.7;CONCLUSION;286
13.1.8;ACKNOWLEDGEMENT;286
13.1.9;REFERENCES;286
13.2;Chapter 2. Boundary Control Approach to the Regularization of a Cauchy Problem for the Heat Equation;288
13.2.1;INTRODUCTION;288
13.2.2;SOLUTION OF PROBLEM (1.5);289
13.2.3;REFERENCES;292
13.3;Chapter 3. How to Tune a Multivariable Pi-controller for Heat Exchangers Using FL^-methods;294
13.3.1;1. INTRODUCTION;294
13.3.2;2.H-OPTIMIZATION;294
13.3.3;3. METHOD TO IMPROVE PI-CONTROLLER;295
13.3.4;4. EXAMPLE;295
13.3.5;5. CONCLUSIONS;296
13.3.6;REFERENCES;296
13.4;Chapter 4. Tracking and Regulation of Periodic Systems;300
13.4.1;INTRODUCTION;300
13.4.2;PRELIMINARIES;300
13.4.3;THE TRACKING PROBLEM;301
13.4.4;THE STOCHASTIC TRACKING PROBLEM;302
13.4.5;EXAMPLES;303
13.4.6;CONCLUSION;304
13.4.7;REFERENCES;304
13.5;Chapter 5. Geometric Theory of Dynamic Systems with Control (CDS);306
13.5.1;INTRODUCTION;306
13.5.2;ANALOGY BETWEEN CDS AND MECHANICAL SYSTEMS (MS);307
13.5.3;REFERENCES;310
13.6;Chapter 6. An Analytical Approach of Optimal Control for Multi-scale Distributed Parameter Systems;312
13.6.1;INTRODUCTION;312
13.6.2;OPTIMAL CONTROL PROBLEM;312
13.6.3;COMPARISON WITH THE GALERKIN METHOD THROUGH AN EXAMPLE;314
13.6.4;CASE OF SINGULARLY PERTURBED SYSTEMS;315
13.6.5;CONCLUSION;316
13.6.6;CALCULATION OF THE ZERO-ORDER APPROXIMATION OF THE OPTIMAL OPERATOR P;316
13.6.7;REFERENCES;318
13.7;Chapter 7. Boundary Control of the Timoshenko Beam with Viscous Internal Dampings;320
13.7.1;1. INTRODUCTION;320
13.7.2;2. MATHEMATICAL FORMULATION;321
13.7.3;3. ANALYTIC SEMIGROUP;322
13.7.4;4. STABILITY OP CONTROL SYSTEM;324
13.7.5;5. CONCLUDING REMARKS;325
13.7.6;REFERENCES;325
14;PART 8: FLEXIBLE SYSTEMS;326
14.1;Chapter 1. Modeling and Control of a Flexible Orbiting Spacecraft;326
14.1.1;INTRODUCTION;326
14.1.2;PROBLEM FORMULATION;326
14.1.3;EQUATIONS OF MOTION;329
14.1.4;STATE EQUATIONS AND FINITEDIMENSIONAL APPROXIMATION;329
14.1.5;REFERENCES;331
14.2;Chapter 2. Non-linear Programming Applicable for the Control of Elastic Structures;332
14.2.1;SHAPE DESIGN PROBLEM;332
14.2.2;BOUNDARY PERTURBATION ANALYSIS;333
14.2.3;DYNAMIC PROGRAM FOR SHAPE OPTIMIZATION;335
14.2.4;NUMERICAL TEST AND CONCLUSIONS;336
14.2.5;REFERENCES;337
14.3;Chapter 3. On Properties of Transfer Functions of a Flexible Structure;338
14.3.1;INTRODUCTION;338
14.3.2;PARTIAL DIFFERENTIAL EQUATION MODEL AND MODAL ANALYSIS;339
14.3.3;MODAL ANALYSIS;339
14.3.4;ANALYSIS BY THE LAPLACE TRANSFORMATION;340
14.3.5;DIFFERENTIAL EQUATION MODEL;340
14.3.6;TRANSFER FUNCTIONS OF CONSTRAINED MODES MODEL;340
14.3.7;TRANSFER FUNCTIONS OF UNCONSTRAINED MODEL;340
14.3.8;POLES AND ZEROS OF THREE KINDS OF RANSFER FUNCTIONS PARTIAL DIFFERENTIAL EQUATION MODEL;340
14.3.9;COMPARISON AMONG TRANSFER FUNCTIONS;341
14.3.10;APPROXIMATION OF TRANSFER FUNCTIONS;341
14.3.11;CONCLUSION;342
14.3.12;REFERENCES;342
14.4;Chapter 4. Experimental Study on Feedback Control of Coupled Bending and Torsional

Vibrations of Flexible Beams;344
14.4.1;1. Introduction;344
14.4.2;2. Dynamic Model;344
14.4.3;3. Feedback Control;345
14.4.4;4. Experimental Devic;346
14.4.5;5. Parameter Identification and Frequency Responses;347
14.4.6;6. Experimental Results;347
14.4.7;7. Concluding Remarks;348
14.4.8;Acknowledgments;348
14.4.9;References;348
14.4.10;Appendix;348
14.5;Chapter 5. The Response of a One-link, Flexible Arm to Variable Structure Control Using Sliding Surfaces;350
14.5.1;INTRODUCTION;350
14.5.2;MODELING APPROACH;351
14.5.3;CONTROL THEORY;352
14.5.4;CONCLUSIONS;354
14.5.5;ACKNOWLEDGEMENT;354
14.5.6;REFERENCES;354
14.6;Chapter 6. Control of Flexible Structures Subject to Random Disturbance;356
14.6.1;1. INTRODUCTION;356
14.6.2;2. MODELS FOR FLEXIBLE SYSTEMS SUBJECT TO RANDOM DISTURBANCE;356
14.6.3;3. REDUCED-ORDER MODELS;357
14.6.4;4. MODAL STATE ESTIMATOR;357
14.6.5;5. MODAL OPTIMAL CONTROL;358
14.6.6;6. SIMULATION STUDIES;358
14.6.7;7. CONCLUSIONS;361
14.6.8;REFERENCES;361
14.6.9;APPENDIX: MODE FREQUENCIES AND MODE SHAPES FOR FREE-FREE EULER-BERNOULLI BEAM;361
14.7;Chapter 7. Eigenstructure Assignment Approach to the Reconfiguration of Flexible Structure Control Systems;362
14.7.1;INTRODUCTION;362
14.7.2;FLEXIBLE STRUCTURE CONTROL;362
14.7.3;FAILURE ACCOMMODATION VIA EIGENSTRUCTURE ASSIGNMENT;363
14.7.4;NUMERICAL EXAMPLE;364
14.7.5;CONCLUSIONS;367
14.7.6;References;367
14.8;Chapter 8. The Q-Parameter Method Applied to the Control of a Flexible Beam;368
14.8.1;1 Introduction;368
14.8.2;2 Controller tuning method;368
14.8.3;3 Beam Control Problem;369
14.8.4;4 Simulation Results;369
14.8.5;5 Conclusions;369
14.8.6;References;370
14.9;Chapter 9. Position and Vibration Controls of Flexible Systems by Means of Tendon Mechanism;372
14.9.1;INTRODUCTION;372
14.9.2;MODELLING;372
14.9.3;CRITERION FUNCTION;373
14.9.4;DESIGN OF CONTROLLER;374
14.9.5;CONTROL CHARACTERISTICS AND SIMULATION;374
14.9.6;CONTROL EXPERIMENT;376
14.9.7;CONCLUSIONS;377
14.9.8;ACKNOWLEDGMENT;377
14.9.9;REFERENCES;377
15;PART 9: COMPUTATIONAL METHODS FOR ESTIMATION IN DPS;378
15.1;Chapter 1. Optimal Weighting for Improving Practical Identiflability in DPS Parameter Estimation Problems;378
15.1.1;INTRODUCTION;378
15.1.2;PRESENTATION OF THE METHOD.;378
15.1.3;GENERAL ANALYSIS OF THE METHOD.;380
15.1.4;REFERENCES;382
15.2;Chapter 2. Statistical Methods for Parameter Identification and Model Selection in Distributed Systems;384
15.2.1;References;386
15.3;Chapter 3. Identification of Degenerate Distributed Parameter Systems;388
15.3.1;1. INTRODUCTION;388
15.3.2;2. THE IDENTIFICATION PROBLEM FOR LINEAR DEGENERATE DISTRIBUTED PARAMETER SYSTEMS;388
15.3.3;3. AN ABSTRACT APPROXIMATION THEORY;389
15.3.4;4. APPLICATIONS TO DEGENERATE PARABOLIC PROBLEMS;390
15.3.5;5. NUMERICAL IMPLEMENTATION;392
15.3.6;6. SUMMARY AND CONCLUDING REMARKS;393
15.3.7;7. REFERENCES;393
15.4;Chapter 4. Identification of Coefficients in Distributed Parameter Models;394
15.4.1;INTRODUCTION;394
15.4.2;BASIC BEAM MODEL;394
15.4.3;DAMPING MODELS;395
15.4.4;PROBLEM STATEMENT;396
15.4.5;RESULTS;396
15.4.6;CONCLUSION AND DISCUSSION;397
15.4.7;ACKNOWLEDGEMENTS;397
15.4.8;REFERENCES;397
15.5;Chapter 5. Estimation of Parameters in Age/Size Structure Population Models;400
15.5.1;1 Introduction;400
15.5.2;2 Cohort dynamics;400
15.5.3;3 The Hackney-Webb method.;401
15.5.4;4 Inverse Problem Techniques;402
15.5.5;5 Simulations and numerical experiments;404
15.5.6;6 Analysis of field data.;404
15.5.7;References;405
16;PART 10: INVERSE TECHNICS IN DPS;406
16.1;Chater 1. Comparison of Space Marching Finite Difference Technique and Function

Minimization Technique for the Estimation of the Front Location in Nonlinear Melting Problem;406
16.1.1;INTRODUCTION;406
16.1.2;PROBLEM STATEMENT;407
16.1.3;DESCRIPTION OF THE METHODS;407
16.1.4;TEST CASES;409
16.1.5;NUMERICAL EXPERIMENTS;409
16.1.6;CONCLUSIONS;411
16.1.7;REFERENCES;411
16.2;Chapter 2. An Observer-based Solution of an Inverse Heat Transfer Problem in Transition Boiling;412
16.2.1;Introduction;412
16.2.2;Problem Description;412
16.2.3;Solution Technique;413
16.2.4;Modeling;413
16.2.5;Observer Equations;414
16.2.6;Implementation, Tuning and Evaluation of the Ob- server;415
16.2.7;Experimental Results;416
16.2.8;Conclusions;417
16.2.9;References;417
16.2.10;Appendix;417
16.2.11;Acknowledgements;417
16.3;Chapter 3. An Inversion Method to Evaluate the Control Law of a Ceramic Kiln;418
16.3.1;Introduction;418
16.3.2;Modelling;418
16.3.3;Direct simulation;418
16.3.4;Inverse problem in the charge;419
16.3.5;Iterative control method;419
16.3.6;Inverse Control Method;420
16.3.7;Conclusion;420
16.3.8;Nomenclature;420
16.3.9;Numerical values;420
16.3.10;References;420
17;PART 11: NONLINEAR SYSTEMS;422
17.1;Chapter 1. Optimal Control of Industrial Sterilization of Canned Foods;422
17.1.1;INTRODUCTION;422
17.1.2;2 . THE OPTIMAL CONTROL PROBLEM;423
17.1.3;3. EXISTENCE AND UNIQUENESS;423
17.1.4;4. OPTIMALITY CONDITIONS;423
17.1.5;5. NUMERICAL SOLUTION;425
17.1.6;6. NUMERICAL RESULTS;425
17.1.7;7. CONCLUSION;426
17.1.8;REFERENCES;426
17.2;Chapter 02.Maximum Principles in the Optimal Control of Semilinear Elliptic Systems;428
17.2.1;INTRODUCTION;428
17.2.2;SETTING OF THE PROBLEM;428
17.2.3;HAMILTONIAN FORMULATION OF THE VARIATION OF THE CRITERION AND PONTRYAGIN'S PRINCIPLE;429
17.2.4;PONTRYAGIN'S PRINCIPLE FOR APPROXIMATE SOLUTIONS;430
17.2.5;REFERENCES;430
17.3;Chapter 3. A Boundary Control Approach to an Optimal Shape Design Problem;432
17.3.1;1. THE PROBLEM;432
17.3.2;2. CONVERTING (P) TO BOUNDARY CONTROL PROBLEM;432
17.3.3;3. PENALIZATION AND REGULARIZATION OF (BP);433
17.3.4;4. OPTIMALITY CONDITIONS FOR PROBLEM (BP*);434
17.3.5;REFERENCES;434
17.4;Chapter 4. Nonlinear Analysis of Dynamics and Control of Interconnected Systems with Distributed Parameters;436
17.4.1;INTRODUCTION;436
17.4.2;1.INTERCONNECTED CONTROL SYSTEM WITH DISTRIBUTED PARAMETERS.;436
17.4.3;2. VECTOR LYAPUNOV FUNCTION AND COMPARISON SYSTEM.;437
17.4.4;3. COMPARISON PRINCIPLE. DERIVATION OF THEOREMS ON DYNAMICAL PROPERTIES.;438
17.4.5;4. THEOREMS ON DYNAMICAL PROPERTIES.;439
17.4.6;5. VLF CONSTRUCTION;440
17.4.7;6.OPTIMAL CONTROL.;441
17.4.8;REFERENCES;443
17.5;Chapter 5. Control of Nonlinear Distributed Parameter Systems Using Fixed Point Theorems:Some New Techniques;444
17.5.1;INTRODUCTION;444
17.5.2;EXAMPLES;444
17.5.3;FIXED POINT THEOREMS;445
17.5.4;CONTROL PROBLEM;445
17.5.5;CONCLUSION;448
17.5.6;REFERENCES;448
17.6;Chapter 6. Quadratic Cost Control for a Class of Non Linear Distributed System;450
17.6.1;1. Introduction;450
17.6.2;2. Statement of the problem;450
17.6.3;3. Bilinearisation theory;450
17.6.4;4. Bilinear quadratic cost control;451
17.6.5;5. Application;452
17.6.6;REFERENCE;454
18;PART 12: DELAY SYSTEMS;456
18.1;Chapter 1. Controllability of Hereditary Differential Functional Systems;456
18.1.1;INTRODUCTION;456
18.1.2;EXEMPLES;456
18.1.3;STATE SPACE THEORY AND PRELIMINARY RESULTS;456
18.1.4;APPROXIMATE CONTROLLABILITY.;459
18.1.5;MATRIX TYPE CONDITIONS;459
18.1.6;REFERENCES;461
18.2;Chapter 2. Commensurate Delay Methods Extended to Independent Delay Problems;462
18.2.1;INTRODUCTION;462
18.2.2;Performance of Predictive Control Schemes;462
18.2.3;Single Delay Calculations: / (h, 0);463
18.2.4;Commensurate Delay Calculations: J (h, h/2);463
18.2.5;Independent Delays: Explicit Taylor series methods;464
18.2.6;Independent Delays: Implicit Taylor series methods;465
18.2.7;Comparison of solutions;466
18.2.8;Conclusions;466
19;PART 13: NUMERICAL TECHNICS;468
19.1;Chapter 1. A Coke Oven Battery Modelization for Transient Operating Conditions;468
19.1.1;INTRODUCTION;468
19.1.2;GUIDELINES FOR MODELLING A SINGLE OVEN;469
19.1.3;VALIDATION OF THE Ml MODEL DURING NOMINAL OPERATING CONDITIONS;470
19.1.4;COKE GAS EVOLUTION AND COKING CHARGE TEMPERATURE;470
19.1.5;OUTPUT MODEL VALIDATION DURING SCHEDULED SHUTDOWN;471
19.1.6;CONCLUSION AND PROSPECTS;471
19.1.7;REFERENCES;471
19.2;Chapter 2. Multilayer Simulation of Heat Flow in a Submerged Arc Furnace Used in the Production of Ferroalloys;476
19.2.1;INTRODUCTION;476
19.2.2;LUMPED PARAMETER MODELS;477
19.2.3;DISTRIBUTED PARAMETER MODELS;478
19.2.4;EXPERT SYSTEM;480
19.2.5;USAGE;480
19.2.6;CONCLUSIONS;481
19.2.7;REFERENCES;481
19.3;Chapter 3. Numerical Approach for Exact Pointwise Controllability of Hyperbolic Systems;482
19.3.1;I - CONSIDERED PROBLEM;482
19.3.2;II - CHOICE OF THE CONTROL;482
19.3.3;III ONE-DIMENSIONAL CASK;483
19.3.4;IV COMPUTATION - EXAMPLES;485
19.3.5;REFERENCES;488
19.4;Chapter 4. On Numerical Results for Shape Optimization ;490
19.4.1;1. INTRODUCTION;490
19.4.2;2. THE PROBLEM;490
19.4.3;3. THE ALGORITHM AND NUMERICAL RESULTS;491
19.4.4;4. FINAL REMARKS;492
19.4.5;REFERENCES;492
20;PART 14: SENSORS AND ACTUATORS;496
20.1;Chapter 1. Sensors Location Problem for Stochastic Non-linear Discrete-time Distributed Parameter Systems;496
20.1.1;INTRODUCTION;496
20.1.2;MODELLING PRELIMINARIES;496
20.1.3;DISCRETE-SCANNING OBSERVATIONS;498
20.1.4;COMPUTATION TECHNIQUE;500
20.1.5;ILUSTRATIVE EXAMPLE;500
20.1.6;CONCLUSION;501
20.1.7;REFERENCES;501
20.2;Chapter 2. Optimization of Sensor and Actuator Locations and Their Sensitivity Analysis;502
20.2.1;I.INTRODUCTION;502
20.2.2;II. PROBLEM STATEMENT;502
20.2.3;111.EXISTENCE THEOREMS;503
20.2.4;IV. NECESSARY AND SUFFICIENT CONDITIONS;503
20.2.5;V. FINITE-DIMENSIONAL APPROXIMATION;505
20.2.6;VI. THE CASE OF SENSOR AND ACTUATOR NOISES;506
20.2.7;VII.SENSITIVITY OF OPTIMAL LOCATIONS;506
20.2.8;IX. CONCLUSIONS;506
20.2.9;REFERENCES;506
21;PART 15: ESTIMATION;15
21.1;Chapter 1. A Posteriori Estimation for One Phase Stefan Problem with Noisy Boundary Input;508
21.1.1;1. Introduction;508
21.1.2;2. Stochastic one phase Stefan problem.;508
21.1.3;3. Onsager-Machlup function.;511
21.1.4;4. Observation mechanism and likelihood functional.;512
21.1.5;5. Maximum a-posteriori estimate;512
21.1.6;6. Conclusions;513
21.1.7;References;513
21.2;Chapter 2. Observers for Distributed-Parameter Systems;514
21.2.1;INTRODUCTION;514
21.2.2;THE GUARANTEED ESTIMATION PROBLEM;514
21.2.3;SENSORS;515
21.2.4;OBSERVABILITY;515
21.2.5;THE INFORMATIONAL DOMAIN;516
21.2.6;INTERRELATION BETWEEN DETERMINISTIC AND STOCHASTIC APPROACHES;516
21.2.7;REFERENCES;517
22;PART 15: MODELLING;518
22.1;Chapter 1. Modelling and Stability Analysis of a Boundary Controlled 2-D Diffusion System;518
22.1.1;Introduction;518
22.1.2;One dimensional approximation;519
22.1.3;Nonharmonic Fourier Series;519
22.1.4;Stability Analysis;520
22.1.5;Results;521
22.1.6;Conclusions;522
22.1.7;References;522
22.2;Chapter 2. Modeling and Control of Distributed Parameter Systems Using a Functional

Approximation Structural Approach;524
22.2.1;INTRODUCTION;524
22.2.2;DISTRIBUTED PARAMETER SYSTEMS FUNCTIONAL APPROXIMATION IN THE FINITE SPACE;524
22.2.3;DETERMINATION OF THE FINITE DIMENTIONS OF THE APPROXIMATED SYSTEM;525
22.2.4;APPLICATION OF THE STRUCTURAL APPROACH IN THE DESCRIPTION OF DISTRIBUTED PARAMETER SYSTEMS IN THE SPACE OF STATES;525
22.2.5;CONNECTING BLOCKS WITH DISTRIBUTED PARAMETERS;526
22.2.6;CONTROLLING THE TEMPERATURE OF AN EXTRUDER LINE FOR POLYAMIDE FIBRES;526
22.2.7;CONCLUSIONS;526
22.2.8;REFERENCES;527
23;Author Index;528
24;Keyword Index;530