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

Haddad, Wassim M.; Nersesov, Sergey G.

Hardcover

ISBN 10: 0691153469 ISBN 13: 9780691153469

Verlag: Princeton University Press, 2011

Inhaltsangabe

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. 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.

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Über die Autorin bzw. den Autor

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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"This solid book provides a unique perspective and detailed account of the theory and applications of vector Lyapunov functions. I am confident it will be well received by researchers and graduate students working in control theory and large-scale systems."--Mehran Mesbahi, University of Washington

"With admirable and sound scholarship, and great scientific maturity, this book gives a methodical development of vector Lyapunov functions and vector control Lyapunov functions for the design of distributed control systems. It is a welcome addition to the literature and develops a rigorous foundation for applications in an important emerging new area."--Frank L. Lewis, University of Texas, Arlington

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"This solid book provides a unique perspective and detailed account of the theory and applications of vector Lyapunov functions. I am confident it will be well received by researchers and graduate students working in control theory and large-scale systems."--Mehran Mesbahi, University of Washington

"With admirable and sound scholarship, and great scientific maturity, this book gives a methodical development of vector Lyapunov functions and vector control Lyapunov functions for the design of distributed control systems. It is a welcome addition to the literature and develops a rigorous foundation for applications in an important emerging new area."--Frank L. Lewis, University of Texas, Arlington

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Stability and Control of Large-Scale Dynamical Systems

A Vector Dissipative Systems ApproachBy Wassim M. Haddad Sergey G. Nersesov

PRINCETON UNIVERSITY PRESS

Copyright © 2011 Princeton University Press
All right reserved.
ISBN: 978-0-691-15346-9

Contents

Preface...............................................................................................................xiiiChapter 1. Introduction...............................................................................................1Chapter 2. Stability Theory via Vector Lyapunov Functions.............................................................9Chapter 3. Large-Scale Continuous-Time Interconnected Dynamical Systems...............................................45Chapter 4. Thermodynamic Modeling of Large-Scale Interconnected Systems...............................................75Chapter 5. Control of Large-Scale Dynamical Systems via Vector Lyapunov Functions.....................................93Chapter 6. Finite-Time Stabilization of Large-Scale Systems via Control Vector Lyapunov Functions.....................107Chapter 7. Coordination Control for Multiagent Interconnected Systems.................................................127Chapter 8. Large-Scale Discrete-Time Interconnected Dynamical Systems.................................................153Chapter 9. Thermodynamic Modeling for Discrete-Time Large-Scale Dynamical Systems.....................................181Chapter 10. Large-Scale Impulsive Dynamical Systems...................................................................211Chapter 11. Control Vector Lyapunov Functions for Large-Scale Impulsive Systems.......................................271Chapter 12. Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems......................................289Chapter 13. Hybrid Decentralized Maximum Entropy Control for Large-Scale Systems......................................305Chapter 14. Conclusion................................................................................................351Bibliography..........................................................................................................353Index.................................................................................................................367

Chapter One

Introduction

1.1 Large-Scale Interconnected Dynamical Systems

Modern complex dynamical systems are highly interconnected and mutually interdependent, both physically and through a multitude of information and communication network constraints. The sheer size (i.e., dimensionality) and complexity of these large-scale dynamical systems often necessitates a hierarchical decentralized architecture for analyzing and controlling these systems. Specifically, in the analysis and control-system design of complex large-scale dynamical systems it is often desirable to treat the overall system as a collection of interconnected subsystems. The behavior of the aggregate or composite (i.e., large-scale) system can then be predicted from the behaviors of the individual subsystems and their interconnections. The need for decentralized analysis and control design of large-scale systems is a direct consequence of the physical size and complexity of the dynamical model. In particular, computational complexity may be too large for model analysis while severe constraints on communication links between system sensors, actuators, and processors may render centralized control architectures impractical. Moreover, even when communication constraints do not exist, decentralized processing may be more economical.

In an attempt to approximate high-dimensional dynamics of large-scale structural (oscillatory) systems with a low-dimensional diffusive (non-oscillatory) dynamical model, structural dynamicists have developed thermodynamic energy flow models using stochastic energy flow techniques. In particular, statistical energy analysis (SEA) predicated on averaging system states over the statistics of the uncertain system parameters have been extensively developed for mechanical and acoustic vibration problems. Thermodynamic models are derived from large-scale dynamical systems of discrete subsystems involving stored energy flow among subsystems based on the assumption of weak subsystem coupling or identical subsystems. However, the ability of SEA to predict the dynamic behavior of a complex large-scale dynamical system in terms of pairwise subsystem interactions is severely limited by the coupling strength of the remaining subsystems on the subsystem pair. Hence, it is not surprising that SEA energy flow predictions for large-scale systems with strong coupling can be erroneous.

Alternatively, a deterministic thermodynamically motivated energy flow modeling for large-scale structural systems is addressed in. This approach exploits energy flow models in terms of thermodynamic energy (i.e., ability to dissipate heat) as opposed to stored energy and is not limited to weak subsystem coupling. Finally, a stochastic energy flow compartmental model (i.e., a model characterized by conservation laws) predicated on averaging system states over the statistics of stochastic system exogenous disturbances is developed in. The basic result demonstrates how compartmental models arise from second-moment analysis of state space systems under the assumption of weak coupling. Even though these results can be potentially applicable to large-scale dynamical systems with weak coupling, such connections are not explored in.

An alternative approach to analyzing large-scale dynamical systems was introduced by the pioneering work of Šiljak and involves the notion of connective stability. In particular, the large-scale dynamical system is decomposed into a collection of subsystems with local dynamics and uncertain interactions. Then, each subsystem is considered independently so that the stability of each subsystem is combined with the interconnection constraints to obtain a vector Lyapunov function for the composite large-scale dynamical system, guaranteeing connective stability for the overall system.

Vector Lyapunov functions were first introduced by Bellman and Matrosov and further developed by Lakshmikantham et al., with exploiting their utility for analyzing large-scale systems. Extensions of vector Lyapunov function theory that include matrix-valued Lyapunov functions for stability analysis of large-scale dynamical systems appear in the monographs by Martynyuk. The use of vector Lyapunov functions in large-scale system analysis offers a very flexible framework for stability analysis since each component of the vector Lyapunov function can satisfy less rigid requirements as compared to a single scalar Lyapunov function. Weakening the hypothesis on the Lyapunov function enlarges the class of Lyapunov functions that can be used for analyzing the stability of large-scale dynamical systems. In particular, each component of a vector Lyapunov function need not be positive definite with a negative or even negative-semidefinite derivative. The time derivative of the vector Lyapunov function need only satisfy an element-by-element vector inequality involving a vector field of a certain comparison system. Moreover, in large-scale systems several Lyapunov functions arise naturally from the stability properties of each subsystem. An alternative approach to vector Lyapunov functions for analyzing large-scale dynamical systems is an input-output approach, wherein stability criteria are derived by assuming that each subsystem is either finite...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 0691153469
• ISBN 13: 9780691153469
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 384
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar