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1st Edition

Stochastic Hybrid Systems




ISBN 9780849390838
Published November 14, 2006 by CRC Press
300 Pages - 49 B/W Illustrations

 
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Book Description

Because they incorporate both time- and event-driven dynamics, stochastic hybrid systems (SHS) have become ubiquitous in a variety of fields, from mathematical finance to biological processes to communication networks to engineering. Comprehensively integrating numerous cutting-edge studies, Stochastic Hybrid Systems presents a captivating treatment of some of the most ambitious types of dynamic systems.

Cohesively edited by leading experts in the field, the book introduces the theoretical basics, computational methods, and applications of SHS. It first discusses the underlying principles behind SHS and the main design limitations of SHS. Building on these fundamentals, the authoritative contributors present methods for computer calculations that apply SHS analysis and synthesis techniques in practice. The book concludes with examples of systems encountered in a wide range of application areas, including molecular biology, communication networks, and air traffic management. It also explains how to resolve practical problems associated with these systems.

Stochastic Hybrid Systems achieves an ideal balance between a theoretical treatment of SHS and practical considerations. The book skillfully explores the interaction of physical processes with computerized equipment in an uncertain environment, enabling a better understanding of sophisticated as well as everyday devices and processes.

Table of Contents

STOCHASTIC HYBRID SYSTEMS: RESEARCH ISSUES AND AREAS
Christos G. Cassandras and John Lygeros
Introduction
Modeling of Nondeterministic Hybrid Systems
Modeling of Stochastic Hybrid Systems
Overview of This Volume
STOCHASTIC DIFFERENTIAL EQUATIONS ON HYBRID STATE SPACES
Jaroslav Krystul, Henk A.P. Blom, and Arunabha Bagchi
Introduction
Semimartingales and Characteristics
Semimartingale Strong Solution of SDE
Stochastic Hybrid Processes as Solutions of SDE
Instantaneous Hybrid Jumps at a Boundary
Related SDE models on Hybrid State Spaces
Markov and Strong Markov Properties
Concluding Remarks
COMPOSITIONAL MODELING OF STOCHASTIC HYBRID SYSTEMS
Stefan Strubbe and Arjan van der Schaft
Introduction
Semantical Models
Communicating PDPs
Conclusions
STOCHASTIC MODEL CHECKING
Joost-Pieter Katoen
Introduction
The Discrete-Time Setting
The Continuous-Time Setting
Bisimulation and Simulation Relations
Epilogue
STOCHASTIC REACHABILITY: THEORY AND NUMERICAL APPROXIMATION
Maria Prandini and Jianghai Hu
Introduction
Stochastic Hybrid System Model
Reachability Problem Formulation
Numerical Approximation Scheme
Reachability Computations
Possible Extensions
Some Examples
Conclusion
STOCHASTIC FLOW SYSTEMS: MODELING AND SENSITIVITY ANALYSIS
Christos G. Cassandras
Introduction
Modeling Stochastic Flow Systems
Sample Paths of Stochastic Flow Systems
Optimization Problems in Stochastic Flow Systems
Infinitesimal Perturbation Analysis (IPA)
Conclusions
PERTURBATION ANALYSIS FOR STOCHASTIC FLOW SYSTEMS WITH FEEDBACK
Yorai Wardi, George Riley, and Richelle Adams
Introduction
SFM with Flow Control
Retransmission-Based Model
Simulation Experiments
Conclusions
STOCHASTIC HYBRID MODELING OF ON-OFF TCP FLOWS
Joao Hespanha
Related Work
A Stochastic Model for TCP
Analysis of the TCP SHS Models
Reduced-Order Models
Conclusions
STOCHASTIC HYBRID MODELING OF BIOCHEMICAL PROCESSES
Panagiotis Kouretas, Konstantinos Koutroumpas, John Lygeros, and Zoi Lygerou
Introduction
Overview of PDMP
Subtilin Production by B. subtilis
DNA Replication in the Cell Cycle
Concluding Remarks
FREE FLIGHT COLLISION RISK ESTIMATION BY SEQUENTIAL MC SIMULATION
Henk A.P. Blom, Jaroslav Krystul, G.J. (Bert) Bakker, Margriet B. Klompstra, and Bart Klein Obbink
Introduction
Sequential MC Estimation of Collision Risk
Development of a Petri Net Model of Free Flight
Simulated Scenarios and Collision Risk Estimates
Concluding Remarks
INDEX

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