Qualitative Theory of Hybrid Dynamical Systems

2000
ISBN: 978-0-8176-4141-2
Verlag: Birkhäuser Boston

Buch, Englisch, 348 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1520 g

Reihe: Control Engineering

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
coverage*application to specific models of manufacturing systems and
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.

Zielgruppe

Research

Autoren/Hrsg.

Savkin, Andrey V.

Matveev, Alexey S.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Produktionstechnik
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Robotik
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Überwachungstechnik

Inhaltsverzeichnis

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.