© 2012

Stochastic Reachability Analysis of Hybrid Systems

  • Provides the reader with state-of-the-art treatment of a powerful new technique for the analysis and control of hybrid systems

  • Coverage of open gives researchers a solid grounding for future work

  • Uses case studies to demonstrate how practising engineers can construct more flexible, reliable and robust systems based on the theory presented


Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Luminita Manuela Bujorianu
    Pages 1-4
  3. Luminita Manuela Bujorianu
    Pages 5-29
  4. Luminita Manuela Bujorianu
    Pages 31-53
  5. Luminita Manuela Bujorianu
    Pages 55-85
  6. Luminita Manuela Bujorianu
    Pages 87-103
  7. Luminita Manuela Bujorianu
    Pages 105-134
  8. Luminita Manuela Bujorianu
    Pages 135-162
  9. Luminita Manuela Bujorianu
    Pages 163-172
  10. Luminita Manuela Bujorianu
    Pages 173-185
  11. Luminita Manuela Bujorianu
    Pages 187-202
  12. Luminita Manuela Bujorianu
    Pages 203-207
  13. Luminita Manuela Bujorianu
    Pages E1-E3
  14. Back Matter
    Pages 209-244

About this book


Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems.

Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then treats issues representing the different faces of SRA:

·        stochastic reachability based on Markov process theory;

·        martingale methods;

·        stochastic reachability as an optimal stopping problem; and

·        dynamic programming.

The book is rounded off by an appendix providing mathematical underpinning on subjects such as ordinary differential equations, probabilistic measure theory and stochastic modeling, which will help the non-expert-mathematician to appreciate the text.

Stochastic Reachability Analysis of Hybrid Systems characterizes a highly interdisciplinary area of research and is consequently of significant interest to academic researchers and graduate students from a variety of backgrounds in control engineering, applied mathematics and computer science.


Autonomous Systems Control Theory Gaussian Processes Hybrid Control Systems Markov Models Markov Processes Model Checking Optimal Control Stochastic Processes Stochastic Reachability

Authors and affiliations

  1. 1.School of MathematicsUniversity of Manchester School of MathematicsManchesterUnited Kingdom

About the authors

Between June 2002 and January 2005, Doctor Bujorianu was a research associate in the Control Group, at the Department of Engineering at the University of Cambridge. After this appointment she remained in the Department as a research visitor for six months. During her appointment at Cambridge, she was involved in two European projects on hybrid systems: the IST-2001-38314 project COLUMBUS: “Design of Embedded Controllers for Safety Critical Systems” (partners: INRIA, University of Berkeley, PARADES (Rome), etc. http; and the IST-2001-32460 project HYBRIDGE: “Distributed Control and Stochastic Analysis of Hybrid Systems Supporting Safety Critical Real-Time Systems Design” (partners: National Aerospace Laboratory-NLR Amsterdam, BAE UK, Eurocontrol, AEA Technology, CENA, etc. http: From November 2005 to June 2008 Doctor Bujorianu was a Research Associate with the Formal Methods and Tools Group at the Faculty of Mathematics and Computer Science, University of Twente, the Netherlands. Her research was funded by the NOW project AiSHA “Abstraction in Stochastic and Hybrid Process Algebra”. During her appointment with University of Twente, she was also involved in the German-Dutch project VOSS. Since June 2008 Manuela Bujorianu has been a Research Associate with the Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA) at the University of Manchester in the UK.

Bibliographic information

  • Book Title Stochastic Reachability Analysis of Hybrid Systems
  • Authors Luminita Manuela Bujorianu
  • Series Title Communications and Control Engineering
  • Series Abbreviated Title Communicat., Control Engineering
  • DOI
  • Copyright Information Springer-Verlag London Limited 2012
  • Publisher Name Springer, London
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-1-4471-2794-9
  • Softcover ISBN 978-1-4471-6209-4
  • eBook ISBN 978-1-4471-2795-6
  • Series ISSN 0178-5354
  • Series E-ISSN 2197-7119
  • Edition Number 1
  • Number of Pages XVIII, 250
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Systems Theory, Control
    Control and Systems Theory
    Math Applications in Computer Science
  • Buy this book on publisher's site
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From the reviews:

“The author presents recent developments in the hybrid stochastic modeling for the analysis of embedded systems. The book starts with a smooth introduction into the problems related to Markovian models. The author defines and characterizes discrete space and continuous space Markov models. … The book is appended by description of some mathematical standard tools that makes it self-contained.” (A. Świerniak, Zentralblatt MATH, Vol. 1245, 2012)