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E-raamat: Qualitative Theory of Hybrid Dynamical Systems

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  • Formaat: PDF+DRM
  • Sari: Control Engineering
  • Ilmumisaeg: 06-Dec-2012
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781461213642
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Qualitative Theory of Hybrid Dynamical SystemsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Control Engineering
  • Ilmumisaeg: 06-Dec-2012
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781461213642
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Hybrid dynamical systems, both continuous and discrete dynamics and variables, have attracted considerable interest recently. This emerging area is found at the interface of control theory and computer engineering, focusing on the analogue and digital aspects of systems and devices. They are essential for advances in modern digital- controller technology. "Qualitative Theory of Hybrid Dynamical Systems" provides a thorough development and systematic presentation of the foundations and framework for hybrid dynamical systems. The presentation offers an accessible, but precise, development of the mathematical models, conditions for existence of limit cycles, and criteria of their stability. The book largely concentrates on the case of discretely controlled continuous-time systems and their relevance for modeling aspects of flexible manufacturing systems and dynamically routed queuing networks. Features and topics: *differential automata*development and use of the concept "cyclic linear differential automata" (CLDA)*switched single-server flow networks queuing networks*select collection of open problems for the subject*self-contained presentation of topics, with the necessary background This new book is an excellent resource for the study and analysis of hybrid dynamical systems used in systems and control engineering. Researchers, postgraduates and professionals in control engineering and computer engineering will find the book an up-to-date development of the relevant new concepts and tools.

Arvustused

"This study investigates the qualitative behaviour of hybrid systems. This evolution is described by the coupling of the dynamics of an ODE and that of an automaton. Once the continuous state reaches a prescribed set S, the state of the automaton switches to another state and another ODE is activated. The main theme is the characterization of periodic behaviour of such systems and, when it is obtained, the study of its stability. This mongraph is an exploration, and its merit is to convince the reader of the difficulty and richness of the topic under investigation." Zentralblatt Math

Muu info

Springer Book Archives
1 Introduction.- 1.1 Hybrid Dynamical Systems.- 1.2 Two Contrasting
Examples of Discretely Controlled Continuous Variable Systems.- 1.3 The Main
Goal of This Book.- 1.4 Organization of the Book.- 1.5 List of Notations.- 2
Qualitative Analysis of Some Simple Hybrid Dynamical Systems.- 2.1
Introduction.- 2.2 Differential Automata and Their Trajectories.- 2.3 Cyclic
Linear Differential Automata.- 2.4 Qualitative Analysis of Cyclic Linear
Differential Automata.- 2.5 Switched Server Systems with a Cyclic Switching
Policy.- 2.6 Switched Server Systems with Several Limit Cycles.- 2.7
Qualitative Analysis of Closed Switched Server Systems.- 2.8 Essentially
Non-Periodic Dynamics of Switched Arrival Systems.- 3 General Theory of
Multivalued Differential Automata.- 3.1 Introduction.- 3.2 Multivalued
Differential Automata.- 3.3 Decomposition of Well-Posed Differential
Automata.- 3.4 Existence of Periodic Trajectories.- 3.5 Proofs of the
Theorems and Lemmas from Section 3.2.- 3.6 Proof of Theorem 3.2.26.- 3.7
Proofs of the Theorems from Sections 3.3 and 3.4.- 4 Two-Dimensional Hybrid
Dynamical Systems.- 4.1 Introduction.- 4.2 An Analog of the Poincaré-Bendixon
Theorem.- 4.3 A Switched Arrival System with Three Buffers.- 4.4 A Switched
Server System with Three Buffers.- 4.5 Proofs of the Statements from Section
4.2.- 5 Limit Cycles in Hybrid Dynamical Systems with Constant Derivatives:
General Theory.- 5.1 Introduction.- 5.2 Basic Assumptions and Definitions.-
5.3 Criteria for Existence and Stability of Limit Cycles.- 5.4 Proofs of the
Lemmas from Section 5.2.- 5.5 Proofs of the Theorems and Lemmas from Section
5.3..- 5.6 Proofs of the Theorem and Lemmas from Subsection 5.3.1.- 6 Limit
Cycles in Hybrid Dynamical Systems with Constant Derivatives: Examples.- 6.1
Introduction.- 6.2Qualitative Analysis of a Switched Server System.- 6.3 A
Switched Arrival System with Three Buffers.- 6.4 Qualitative Analysis of
Switched Single Server Flow Networks.- 7 Globally Periodic Behavior of
Switched Single Server Flow Networks.- 7.1 Introduction.- 7.2 Description of
Switched Single Server Flow Networks.- 7.3 Analysis of Switched Single Server
Flow Networks.- 8 Regularizability of Switched Multiple Server Flow
Networks.- 8.1 Introduction 315 8.2 Description of Switched Multiple Server
Flow Networks.- 8.3 Regularizable Switched Multiple Server Flow Networks.-
8.4 Illustrative Example.- 9 Open Problems.- 9.1 Introduction.- 9.2 Switched
Server Systems.- 9.3 Essentially Nonperiodic Multidimensional Switched
Arrival Systems.- 9.4 Switched Server/Arrival Systems with Several Servers.-
9.5 A Generalized Processor Sharing Model.- 9.6 Stabilizability of Switched
Multiple Server Flow Networks.- 9.7 Chaotic Switched Flow Networks.- 9.8
Existence and Global Stability of Limit Cycles in Nonlinear Differential
Automata.- References.
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