Stochastic Hybrid Systems: 1st Edition (Hardback) book cover

Stochastic Hybrid Systems

1st Edition

Edited by Christos G. Cassandras, John Lygeros

CRC Press

304 pages | 49 B/W Illus.

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Hardback: 9780849390838
pub: 2006-11-14
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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

About the Series

Automation and Control Engineering

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Subject Categories

BISAC Subject Codes/Headings:
TEC007000
TECHNOLOGY & ENGINEERING / Electrical