Stability and Control of Large-Scale Dynamical Systems

Preface xiiiCHAPTER 1. Introduction 11.1 Large-Scale Interconnected Dynamical Systems 11.2 A Brief Outline of the Monograph 5CHAPTER 2. Stability Theory via Vector Lyapunov Functions 92.1 Introduction 92.2 Notation and Definitions 92.3 Quasi-Monotone and Essentially Nonnegative Vector Fields 102.4 Generalized Differential Inequalities 142.5 Stability Theory via Vector Lyapunov Functions 182.6 Discrete-Time Stability Theory via Vector Lyapunov Functions 34CHAPTER 3. Large-Scale Continuous-Time Interconnected Dynamical Systems 453.1 Introduction 453.2 Vector Dissipativity Theory for Large-Scale Nonlinear Dynamical Systems 463.3 Extended Kalman-Yakubovich-Popov Conditions for Large- Scale Nonlinear Dynamical Systems 613.4 Specialization to Large-Scale Linear Dynamical Systems 683.5 Stability of Feedback Interconnections of Large-Scale Nonlinear Dynamical Systems 71CHAPTER 4. Thermodynamic Modeling of Large-Scale Interconnected Systems 754.1 Introduction 754.2 Conservation of Energy and the First Lawof Thermodynamics 754.3 Nonconservation of Entropy and the Second Law of Thermodynamics 794.4 Semistability and Large-Scale Systems 824.5 Energy Equipartition 864.6 Entropy Increase and the Second Law of Thermodynamics 884.7 Thermodynamic Models with Linear Energy Exchange 90CHAPTER 5. Control of Large-Scale Dynamical Systems via Vector Lyapunov Functions 935.1 Introduction 935.2 Control Vector Lyapunov Functions 945.3 Stability Margins, Inverse Optimality, and Vector Dissipativity 995.4 Decentralized Control for Large-Scale Nonlinear Dynamical Systems 102CHAPTER 6. Finite-Time Stabilization of Large-Scale Systems via Control Vector Lyapunov Functions 1076.1 Introduction 1076.2 Finite-Time Stability via Vector Lyapunov Functions 1086.3 Finite-Time Stabilization of Large-Scale Dynamical Systems 1146.4 Finite-Time Stabilization for Large-Scale Homogeneous Systems 1196.5 Decentralized Control for Finite-Time Stabilization of Large-Scale Systems 121CHAPTER 7. Coordination Control for Multiagent Interconnected Systems 1277.1 Introduction 1277.2 Stability and Stabilization of Time-Varying Sets 1297.3 Control Design for Multivehicle Coordinated Motion 1357.4 Stability and Stabilization of Time-Invariant Sets 1417.5 Control Design for Static Formations 1447.6 Obstacle Avoidance in Multivehicle Coordination 145CHAPTER 8. Large-Scale Discrete-Time Interconnected Dynamical Systems 1538.1 Introduction 1538.2 Vector Dissipativity Theory for Discrete-Time Large-Scale Nonlinear Dynamical Systems 1548.3 Extended Kalman-Yakubovich-Popov Conditions for Discrete- Time Large-Scale Nonlinear Dynamical Systems 1688.4 Specialization to Discrete-Time Large-Scale Linear Dynamical Systems 1738.5 Stability of Feedback Interconnections of Discrete-Time Large-Scale Nonlinear Dynamical Systems 177CHAPTER 9. Thermodynamic Modeling for Discrete-Time Large-Scale Dynamical Systems 1819.1 Introduction 1819.2 Conservation of Energy and the First Law of Thermodynamics 1829.3 Nonconservation of Entropy and the Second Law of Thermodynamics 1879.4 Nonconservation of Ectropy 1899.5 Semistability of Discrete-Time Thermodynamic Models 1919.6 Entropy Increase and the Second Law of Thermodynamics 1989.7 Thermodynamic Models with Linear Energy Exchange 200CHAPTER 10. Large-Scale Impulsive Dynamical Systems 21110.1 Introduction 21110.2 Stability of Impulsive Systems via Vector Lyapunov Functions 21310.3 Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems 22410.4 Extended Kalman-Yakubovich-Popov Conditions for Large- Scale Impulsive Dynamical Systems 24910.5 Specialization to Large-Scale Linear Impulsive Dynamical Systems 25910.6 Stability of Feedback Interconnections of Large-Scale Impulsive Dynamical Systems 264CHAPTER 11. Control Vector Lyapunov Functions for Large-Scale Impulsive Systems 27111.1 Introduction 27111.2 Control Vector Lyapunov Functions for Impulsive Systems 27211.3 Stability Margins and Inverse Optimality 27911.4 Decentralized Control for Large-Scale Impulsive Dynamical Systems 284CHAPTER 12. Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems 28912.1 Introduction 28912.2 Finite-Time Stability of Impulsive Dynamical Systems 28912.3 Finite-Time Stabilization of Impulsive Dynamical Systems 29712.4 Finite-Time Stabilizing Control for Large-Scale Impulsive Dynamical Systems 300CHAPTER 13. Hybrid Decentralized Maximum Entropy Control for Large-Scale Systems 30513.1 Introduction 30513.2 Hybrid Decentralized Control and Large-Scale Impulsive Dynamical Systems 30613.3 Hybrid Decentralized Control for Large-Scale Dynamical Systems 31313.4 Interconnected Euler-Lagrange Dynamical Systems 31913.5 Hybrid Decentralized Control Design 32313.6 Quasi-Thermodynamic Stabilization and Maximum Entropy Control 32713.7 Hybrid Decentralized Control for Combustion Systems 33513.8 Experimental Verification of Hybrid Decentralized Controller 341CHAPTER 14. Conclusion 351Bibliography 353Index 367