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E-raamat: Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

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Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems ApproachSuurem pilt
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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.

Arvustused

Wassim Haddad, Winner of the 2014 Pendray Aerospace Literature Award, American Institute of Aeronautics and Astronautics "The monograph is an excellent up-to-date authoritative reference covering original results which are presented in a rigorous, unified framework with examples... The book will be useful primarily to applied mathematicians, control theorists and engineers, and anyone dealing with Lyapunov stability and control of nonlinear interconnected dynamic systems."--Lubomir Bakule, Zentralblatt MATH

Preface xiii
Chapter 1 Introduction
1(8)
1.1 Large-Scale Interconnected Dynamical Systems
1(4)
1.2 A Brief Outline of the Monograph
5(4)
Chapter 2 Stability Theory via Vector Lyapunov Functions
9(36)
2.1 Introduction
9(1)
2.2 Notation and Definitions
9(1)
2.3 Quasi-Monotone and Essentially Nonnegative Vector Fields
10(4)
2.4 Generalized Differential Inequalities
14(4)
2.5 Stability Theory via Vector Lyapunov Functions
18(16)
2.6 Discrete-Time Stability Theory via Vector Lyapunov Functions
34(11)
Chapter 3 Large-Scale Continuous-Time Interconnected Dynamical Systems
45(30)
3.1 Introduction
45(1)
3.2 Vector Dissipativity Theory for Large-Scale Nonlinear Dynamical Systems
46(15)
3.3 Extended Kalman-Yakubovich-Popov Conditions for Large-Scale Nonlinear Dynamical Systems
61(7)
3.4 Specialization to Large-Scale Linear Dynamical Systems
68(3)
3.5 Stability of Feedback Interconnections of Large-Scale Nonlinear Dynamical Systems
71(4)
Chapter 4 Thermodynamic Modeling of Large-Scale Interconnected Systems
75(18)
4.1 Introduction
75(1)
4.2 Conservation of Energy and the First Law of Thermodynamics
75(4)
4.3 Nonconservation of Entropy and the Second Law of Thermodynamics
79(3)
4.4 Semistability and Large-Scale Systems
82(4)
4.5 Energy Equipartition
86(2)
4.6 Entropy Increase and the Second Law of Thermodynamics
88(2)
4.7 Thermodynamic Models with Linear Energy Exchange
90(3)
Chapter 5 Control of Large-Scale Dynamical Systems via Vector Lyapunov Functions
93(14)
5.1 Introduction
93(1)
5.2 Control Vector Lyapunov Functions
94(5)
5.3 Stability Margins, Inverse Optimality, and Vector Dissi-pativity
99(3)
5.4 Decentralized Control for Large-Scale Nonlinear Dynamical Systems
102(5)
Chapter 6 Finite-Time Stabilization of Large-Scale Systems via Control Vector Lyapunov Functions
107(20)
6.1 Introduction
107(1)
6.2 Finite-Time Stability via Vector Lyapunov Functions
108(6)
6.3 Finite-Time Stabilization of Large-Scale Dynamical Systems
114(5)
6.4 Finite-Time Stabilization for Large-Scale Homogeneous Systems
119(2)
6.5 Decentralized Control for Finite-Time Stabilization of Large-Scale Systems
121(6)
Chapter 7 Coordination Control for Multiagent Interconnected Systems
127(26)
7.1 Introduction
127(2)
7.2 Stability and Stabilization of Time-Varying Sets
129(6)
7.3 Control Design for Multivehicle Coordinated Motion
135(6)
7.4 Stability and Stabilization of Time-Invariant Sets
141(3)
7.5 Control Design for Static Formations
144(1)
7.6 Obstacle Avoidance in Multivehicle Coordination
145(8)
Chapter 8 Large-Scale Discrete-Time Interconnected Dynamical Systems
153(28)
8.1 Introduction
153(1)
8.2 Vector Dissipativity Theory for Discrete-Time Large-Scale Nonlinear Dynamical Systems
154(14)
8.3 Extended Kalman-Yakubovich-Popov Conditions for Discrete-Time Large-Scale Nonlinear Dynamical Systems
168(5)
8.4 Specialization to Discrete-Time Large-Scale Linear Dynamical Systems
173(4)
8.5 Stability of Feedback Interconnections of Discrete-Time Large-Scale Nonlinear Dynamical Systems
177(4)
Chapter 9 Thermodynamic Modeling for Discrete-Time Large-Scale Dynamical Systems
181(30)
9.1 Introduction
181(1)
9.2 Conservation of Energy and the First Law of Thermodynamics
182(5)
9.3 Nonconservation of Entropy and the Second Law of Thermodynamics
187(2)
9.4 Nonconservation of Ectropy
189(2)
9.5 Semistability of Discrete-Time Thermodynamic Models
191(7)
9.6 Entropy Increase and the Second Law of Thermodynamics
198(2)
9.7 Thermodynamic Models with Linear Energy Exchange
200(11)
Chapter 10 Large-Scale Impulsive Dynamical Systems
211(60)
10.1 Introduction
211(2)
10.2 Stability of Impulsive Systems via Vector Lyapunov Functions
213(11)
10.3 Vector Dissipativity Theory for Large-Scale Impulsive Dynamical Systems
224(25)
10.4 Extended Kalman-Yakubovich-Popov Conditions for Large-Scale Impulsive Dynamical Systems
249(10)
10.5 Specialization to Large-Scale Linear Impulsive Dynamical Systems
259(5)
10.6 Stability of Feedback Interconnections of Large-Scale Impulsive Dynamical Systems
264(7)
Chapter 11 Control Vector Lyapunov Functions for Large-Scale Impulsive Systems
271(18)
11.1 Introduction
271(1)
11.2 Control Vector Lyapunov Functions for Impulsive Systems
272(7)
11.3 Stability Margins and Inverse Optimality
279(5)
11.4 Decentralized Control for Large-Scale Impulsive Dynamical Systems
284(5)
Chapter 12 Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems
289(16)
12.1 Introduction
289(1)
12.2 Finite-Time Stability of Impulsive Dynamical Systems
289(8)
12.3 Finite-Time Stabilization of Impulsive Dynamical Systems
297(3)
12.4 Finite-Time Stabilizing Control for Large-Scale Impulsive Dynamical Systems
300(5)
Chapter 13 Hybrid Decentralized Maximum Entropy Control for Large-Scale Systems
305(46)
13.1 Introduction
305(1)
13.2 Hybrid Decentralized Control and Large-Scale Impulsive Dynamical Systems
306(7)
13.3 Hybrid Decentralized Control for Large-Scale Dynamical Systems
313(6)
13.4 Interconnected Euler-Lagrange Dynamical Systems
319(4)
13.5 Hybrid Decentralized Control Design
323(4)
13.6 Quasi-Thermodynamic Stabilization and Maximum Entropy Control
327(8)
13.7 Hybrid Decentralized Control for Combustion Systems
335(6)
13.8 Experimental Verification of Hybrid Decentralized Controller
341(10)
Chapter 14 Conclusion
351(2)
Bibliography 353(14)
Index 367
Wassim M. Haddad is a professor in the School of Aerospace Engineering and chair of the Flight Mechanics and Control Discipline at Georgia Institute of Technology. Sergey G. Nersesov is an associate professor in the Department of Mechanical Engineering at Villanova University.
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