Advanced Topics in Control Systems Theory: Lecture Notes from FAP 2004

✍ Scribed by F. Lamnabhi-Lagarrigue, A. Lor´ıa, E. Panteley (Eds.)

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 216
• Series: Lecture Notes in Control and Information Sciences volume 311
• Edition: 1st Edition.
• Category: Library

✦ Synopsis

"Advanced Topics in Control Systems Theory" contains selected contributions written by lecturers at the second (annual) Formation d’Automatique de Paris (FAP) (Graduate Control School in Paris). It is addressed to graduate students and researchers in control theory with topics touching on a variety of areas of interest to the control community such as cascaded systems, flatness, optimal control, and Hamiltonian and infinite-dimensional systems. The reader is provided with a well-integrated synthesis of the latest thinking in these subjects without the need for an exhaustive literature review. "Advanced Topics in Control Systems Theory" can be used to support either a one-term general advanced course on nonlinear control theory, devoting a few lectures to each chapter, or for more focused and intensive courses at graduate level. The book’s concise but pedagogical manner will give an ideal start to researchers wishing to broaden their knowledge in aspects of modern control theory outside their own expertise.

✦ Table of Contents

Advanced Topics in Control Systems Theory, Lecture Notes from FAP 2004......Page 1
2 Cascaded Nonlinear Time-Varying Systems Analysis and Design......Page 15
2.1 Preliminaries on Time-Varying Systems......Page 16
2.1.1 Stability De.nitions......Page 17
2.1.2 Why Uniform Stability?......Page 19
2.2.1 Introduction......Page 21
2.2.2 Peaking: A Technical Obstacle to Analysis......Page 23
2.2.3 Control Design from a Cascades Point of View......Page 25
2.3.1 Brief Literature Review......Page 28
2.3.2 Nonautonomous Cascades: Problem Statement......Page 30
2.3.3 Basic Assumptions and Results......Page 31
2.3.4 An Integrability Criterion......Page 35
2.3.5 Growth Rate Theorems......Page 36
2.4 Applications in Control Design......Page 40
2.4.1 Output Feedback Dynamic Positioning of a Ship......Page 41
2.4.2 Pressure Stabilization of a Turbo-Diesel Engine......Page 43
2.4.3 Nonholonomic Systems......Page 46
2.5 Conclusions......Page 52
References......Page 53
3.1 Introduction......Page 57
3.2 Mathematical Models......Page 59
3.2.1 The Attitude Control Problem......Page 60
3.2.2 Orbital Transfer......Page 61
3.2.3 Shuttle Re-entry......Page 63
3.3.1 Poisson Stability......Page 65
3.3.2 General Results About Controllability......Page 66
3.3.3 Controllability and Enlargement Technique (Jurdjevi´c-Kupka)......Page 68
3.3.5 Application to the Orbital Transfer......Page 69
3.4.1 Stabilization Techniques......Page 70
3.4.2 Path Planning......Page 74
3.5.2 Weak Maximum Principle......Page 76
3.5.3 Maximum Principle......Page 78
3.5.4 Extremals in SR-Geometry......Page 79
3.5.5 SR-Systems with Drift......Page 80
3.5.6 Extremals for Single-Input A.ne Systems......Page 85
3.5.7 Second-Order Conditions......Page 87
3.5.8 Optimal Controls with State Constraints......Page 93
3.6.1 Shooting Techniques......Page 101
3.6.2 Second-Order Algorithms in Orbital Transfer......Page 104
References......Page 105
4.1 Introduction......Page 106
4.2 Systems of Two Physical Domains in Canonical Interaction......Page 108
4.2.1 Conservation Laws, Interdomain Coupling and Boundary Energy Flows: Motivational Examples......Page 109
4.3.1 Dirac Structures......Page 120
4.3.2 Stokes-Dirac Structures......Page 121
4.3.3 Poisson Brackets Associated to Stokes-Dirac Structures......Page 123
4.4.1 Boundary Port-Hamiltonian Systems......Page 125
4.4.2 Boundary Port-Hamiltonian Systems with Distributed Ports and Dissipation......Page 127
4.5.1 Maxwell’s Equations......Page 129
4.5.2 Telegraph Equations......Page 131
4.6.2 Ideal Isentropic Fluid......Page 134
4.7 Conserved Quantities......Page 139
4.8 Conclusions and Final Remarks......Page 142
References......Page 143
5.1 Introduction......Page 146
5.2 Motivating Examples......Page 152
5.3 Algebraic Analysis......Page 159
5.4 Problem Formulation......Page 188
5.5 Problem Solution......Page 191
5.6 Poles and Zeros......Page 202
5.8 Exercises......Page 211
References......Page 213
back-matter......Page 215