Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach(Princeton Series in Applied Mathematics)

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.

Table of Contents:
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-Scale Impulsive Dynamical Systems 264 CHAPTER 11. Control Vector Lyapunov Functions for Large-Scale Impulsive Systems 271 11.1 Introduction 271 11.2 Control Vector Lyapunov Functions for Impulsive Systems 272 11.3 Stability Margins and Inverse Optimality 279 11.4 Decentralized Control for Large-Scale Impulsive Dynamical Systems 284 CHAPTER 12. Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems 289 12.1 Introduction 289 12.2 Finite-Time Stability of Impulsive Dynamical Systems 289 12.3 Finite-Time Stabilization of Impulsive Dynamical Systems 297 12.4 Finite-Time Stabilizing Control for Large-Scale Impulsive Dynamical Systems 300 CHAPTER 13. Hybrid Decentralized Maximum Entropy Control for Large-Scale Systems 305 13.1 Introduction 305 13.2 Hybrid Decentralized Control and Large-Scale Impulsive Dynamical Systems 306 13.3 Hybrid Decentralized Control for Large-Scale Dynamical Systems 313 13.4 Interconnected Euler-Lagrange Dynamical Systems 319 13.5 Hybrid Decentralized Control Design 323 13.6 Quasi-Thermodynamic Stabilization and Maximum Entropy Control 327 13.7 Hybrid Decentralized Control for Combustion Systems 335 13.8 Experimental Verification of Hybrid Decentralized Controller 341 CHAPTER 14. Conclusion 351 Bibliography 353 Index 367