Buch, Englisch, 392 Seiten, Format (B × H): 180 mm x 254 mm, Gewicht: 975 g
A Vector Dissipative Systems Approach
Buch, Englisch, 392 Seiten, Format (B × H): 180 mm x 254 mm, Gewicht: 975 g
Reihe: Princeton Series in Applied Mathematics
ISBN: 978-0-691-15346-9
Verlag: Princeton University Press
Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
- Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik
- Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
Weitere Infos & Material
Preface xiii
CHAPTER 1. Introduction 1
1.1 Large-Scale Interconnected Dynamical Systems 1
1.2 A Brief Outline of the Monograph 5
CHAPTER 2. Stability Theory via Vector Lyapunov Functions 9
2.1 Introduction 9
2.2 Notation and Definitions 9
2.3 Quasi-Monotone and Essentially Nonnegative Vector Fields 10
2.4 Generalized Differential Inequalities 14
2.5 Stability Theory via Vector Lyapunov Functions 18
2.6 Discrete-Time Stability Theory via Vector Lyapunov Functions 34
CHAPTER 3. Large-Scale Continuous-Time Interconnected Dynamical Systems 45
3.1 Introduction 45
3.2 Vector Dissipativity Theory for Large-Scale Nonlinear Dynamical Systems 46
3.3 Extended Kalman-Yakubovich-Popov Conditions for Large- Scale Nonlinear Dynamical Systems 61
3.4 Specialization to Large-Scale Linear Dynamical Systems 68
3.5 Stability of Feedback Interconnections of Large-Scale Nonlinear Dynamical Systems 71
CHAPTER 4. Thermodynamic Modeling of Large-Scale Interconnected Systems 75
4.1 Introduction 75
4.2 Conservation of Energy and the First Law
of Thermodynamics 75
4.3 Nonconservation of Entropy and the Second Law of Thermodynamics 79
4.4 Semistability and Large-Scale Systems 82
4.5 Energy Equipartition 86
4.6 Entropy Increase and the Second Law of Thermodynamics 88
4.7 Thermodynamic Models with Linear Energy Exchange 90
CHAPTER 5. Control of Large-Scale Dynamical Systems via Vector Lyapunov Functions 93
5.1 Introduction 93
5.2 Control Vector Lyapunov Functions 94
5.3 Stability Margins, Inverse Optimality, and Vector Dissipativity 99
5.4 Decentralized Control for Large-Scale Nonlinear Dynamical Systems 102
CHAPTER 6. Finite-Time Stabilization of Large-Scale Systems via Control Vector Lyapunov Functions 107
6.1 Introduction 107
6.2 Finite-Time Stability via Vector Lyapunov Functions 108
6.3 Finite-Time Stabilization of Large-Scale Dynamical Systems 114
6.4 Finite-Time Stabilization for Large-Scale Homogeneous Systems 119
6.5 Decentralized Control for Finite-Time Stabilization of Large-Scale Systems 121
CHAPTER 7. Coordination Control for Multiagent Interconnected Systems 127
7.1 Introduction 127
7.2 Stability and Stabilization of Time-Varying Sets 129
7.3 Control Design for Multivehicle Coordinated Motion 135
7.4 Stability and Stabilization of Time-Invariant Sets 141
7.5 Control Design for Static Formations 144
7.6 Obstacle Avoidance in Multivehicle Coordination 145
CHAPTER 8. Large-Scale Discrete-Time Interconnected Dynamical Systems 153
8.1 Introduction 153
8.2 Vector Dissipativity Theory for Discrete-Time Large-Scale Nonlinear Dynamical Systems 154
8.3 Extended Kalman-Yakubovich-Popov Conditions for Discrete- Time Large-Scale Nonlinear Dynamical Systems 168
8.4 Specialization to Discrete-Time Large-Scale Linear Dynamical Systems 173
8.5 Stability of Feedback Interconnections of Discrete-Time Large-Scale Nonlinear Dynamical Systems 177
CHAPTER 9. Thermodynamic Modeling for Discrete-Time Large-Scale Dynamical Systems 181
9.1 Introduction 181
9.2 Conservation of Energy and the First Law of Thermodynamics 182
9.3 Nonconservation of Entropy and the Second Law of Thermodynamics 187
9.4 Nonconservation of Ectropy 189
9.5 Semistability of Discrete-Time Thermodynamic Models 191
9.6 Entropy Increase and the Second Law of Thermodynamics 198
9.7 Thermodynamic Models with Linear Energy Exchange 200
CHAPTER 10. Large-Scale Impulsive Dynamical Systems 211
10.1 Introduction 211
10.2 Stability of Impulsive Systems via Vector Lyapunov Functions 213
10.3 Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems 224
10.4 Extended Kalman-Yakubovich-Popov Conditions for Large- Scale Impulsive Dynamical Systems 249
10.5 Specialization to Large-Scale Linear Impulsive Dynamical Systems 259
10.6 Stability of Feedback Interconnections of Large-Scal
