Stochastic Hybrid Systems

Stochastic Hybrid Systems

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Features

  • Integrates the most recent research results of SHS
  • Addresses fundamental issues that include unifying modeling frameworks and abstractions of complex SHS
  • Illustrates computational methods for the analysis of SHS, including model checking, numerical, and Monte Carlo techniques
  • Includes advanced application areas, such as computer networks and biological processes, to illustrate how the theoretical foundations can be used in practice
  • Summary

    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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