Belmiloudi Stabilization, Optimal and Robust Control

Theory and Applications in Biological and Physical Sciences
1. Auflage 2008
ISBN: 978-1-84800-344-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 502 Seiten

Reihe: Communications and Control Engineering

Stabilization, Optimal and Robust Control develops robust control of infinite-dimensional dynamical systems derived from time-dependent coupled PDEs associated with boundary-value problems. Rigorous analysis takes into account nonlinear system dynamics, evolutionary and coupled PDE behaviour and the selection of function spaces in terms of solvability and model quality. Mathematical foundations are provided so that the book remains accessible to the non-control-specialist. Following chapters giving a general view of convex analysis and optimization and robust and optimal control, problems arising in fluid mechanical, biological and materials scientific systems are laid out in detail. The combination of mathematical fundamentals with application of current interest will make this book of much interest to researchers and graduate students looking at complex problems in mathematics, physics and biology as well as to control theorists.

Autoren/Hrsg.

Belmiloudi, Aziz

Inhaltsverzeichnis

1;Preface;7
2;Contents;11
3;Notation and Symbols;18
4;1 General Introduction;21
4.1;1.1 Motivations and Objectives;22
4.2;1.2 General Process of the Robust Control Theory;26
4.3;1.3 Applications to Biological and Physical Sciences;27
5;Part I Convex Analysis and Duality Principles;31
5.1;2 Convexity and Topology;32
5.1.1;2.1 Convex Sets;32
5.1.2;2.2 Convex Functions;38
5.1.3;2.3 G-Regularization and Continuous Affine Functions;58
5.2;3 A Brief Overview of Sobolev Spaces;61
5.2.1;3.1 Tools and Definitions;61
5.2.2;3.2 Some Properties of Sobolev Spaces;67
5.3;4 Legendre–Fenchel Transformation and Duality;74
5.3.1;4.1 Fenchel Conjugate Functions;74
5.3.2;4.2 Subdifferentials and Superdifferentials of Extended-value Functions;79
5.3.3;4.3 Applications of the Duality;94
5.4;5 Lagrange Duality Theory;116
5.4.1;5.1 Frenchel–Rockafellar Duality in Optimization;116
5.4.2;5.2 Lagrange Duality;125
5.4.3;5.3 Minimax Duality;143
5.4.4;5.4 Duality and Parametric Variational Problems;164
6;Part II General Results and Concepts on Robust and Optimal Control Theory for Evolutive Systems;177
6.1;6 Studied Systems and General Results;178
6.1.1;6.1 Hypotheses and Properties;178
6.1.2;6.2 Evolution Problems, Existence and Stability Results;181
6.1.3;6.3 Regularity Results;186
6.1.4;6.4 Examples of Operators and Spaces;192
6.2;7 Optimal Control Problems;198
6.2.1;7.1 Introduction;198
6.2.2;7.2 Basic Framework;199
6.2.3;7.3 Linear Control Problems;202
6.2.4;7.4 Examples of Controls and Observations;208
6.2.5;7.5 Parameter Estimations and Bilinear Control Problems;217
6.2.6;7.6 Non-linear Control for Non-linear Evolutive PDE Problems;223
6.3;8 Stabilization and Robust Control Problem;241
6.3.1;8.1 Motivation and Objectives;241
6.3.2;8.2 Basic Framework;243
6.3.3;8.3 Linear Robust Control Problems;246
6.3.4;8.4 Examples of Controls, Disturbances and Observations;254
6.3.5;8.5 Bilinear-type Robust Control Problems;267
6.3.6;8.6 Non-linear Robust Control for Non-linear Evolutive Problems;280
6.3.7;8.7 Non-linear Time-varying Delay Systems;310
6.4;9 Remarks on Numerical Techniques;332
6.4.1;9.1 Introduction and Studied Problem;332
6.4.2;9.2 Continuous Case;334
6.4.3;9.3 Discrete Problem;341
7;Part III Applications in the Biological and Physical Sciences: Modeling and Stabilization;348
7.1;10 Vortex Dynamics in Superconductors and Ginzburg–Landau-type Models;351
7.1.1;10.1 Introduction;351
7.1.2;10.2 Existence and Uniqueness of the Solution of the MTDGL Model;357
7.1.3;10.3 The Perturbation Problem;358
7.1.4;10.4 Differentiability of the Operator Solution;360
7.1.5;10.5 Robust Control Problems;362
7.2;11 Multi-scale Modeling of Alloy Solidification and Phase-field Model;381
7.2.1;11.1 Introduction;382
7.2.2;11.2 Existence, Uniqueness and a Maximum Principle;388
7.2.3;11.3 The Perturbation Problem;390
7.2.4;11.4 Differentiability of the Operator Solution;392
7.2.5;11.5 Robust Control Problems;394
7.3;12 Large-scale Ocean in the Climate System;406
7.3.1;12.1 Introduction and Formulation of the Problem;406
7.3.2;12.2 The Perturbation Problem;411
7.3.3;12.3 Robust Control Problems;421
7.3.4;12.4 Primitive Ocean Equations with Vertical Viscosity;429
7.4;13 Heat Transfer Laws on Temperature Distribution in Biological Tissues;437
7.4.1;13.1 Introduction;437
7.4.2;13.2 The State System;442
7.4.3;13.3 The Perturbation Problem;447
7.4.4;13.4 Robust Control Problems;449
7.4.5;13.5 Other Situations;455
7.5;14 Lotka–Volterra-type Systems with Logistic Time-varying Delays;460
7.5.1;14.1 Introduction and Mathematical Setting;460
7.5.2;14.2 Existence and Uniqueness of the Solution;463
7.5.3;14.3 The Perturbation Problem;468
7.5.4;14.4 Robust Control Problems;469
7.5.5;14.5 Other Situations;477
7.6;15 Other Systems;482
7.6.1;15.1 Micropolar Fluids and Blood Pressure;482
7.6.2;15.2 Semiconductor Melt Flow in Crystal Growth;487
8;References;491
9;Index;506