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Formal Methods for Discrete-Time Dynamical Systems

  • Book
  • © 2017


  • Provides a self-contained exposition of temporal logic control for finite nondeterministic systems, which are useful even for seasoned formal methods researchers
  • Presents formal verification and control algorithms for discrete-time dynamical systems
  • Intended for a broad audience of scientists and engineers interested in formal methods and controls
  • Includes supplementary material:

Part of the book series: Studies in Systems, Decision and Control (SSDC, volume 89)

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About this book

This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models.

The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.

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Table of contents (12 chapters)

  1. Transition Systems, Automata, and Temporal Logics

  2. Analysis and Control of Finite Transition Systems

  3. Analysis and Control of Discrete-Time Dynamical Systems


“This work is suitable both for researchers from these fields, and also young graduates, provided they are familiar with fundamental concepts of systems theory and theoretical computer science. A strong feature of this work is its plethora of examples, which greatly help in understanding the presented theory, and also help the reader get an idea for the applications that can be considered.” (Lazaros Moysis, zbMATH 1409.93003, 2019)

“The book under review gives an introduction to and overview of particular verification methods for models of systems that evolve in discrete time and usually have unbounded state spaces. … The book can serve as a textbook for an advanced and specialised graduate course in formal methods or control theory.” (Martin Lange, Mathematical Reviews, February, 2018)

Authors and Affiliations

  • Boston University, Mechanical Engineering, Electrical and Computer Engineering, and Systems Engineering, Boston, USA

    Calin Belta

  • Microsoft Research Ltd, Biological Computation Group, Cambridge, United Kingdom

    Boyan Yordanov

  • Middle East Technical University, Department of Computer Engineering, Cankaya, Turkey

    Ebru Aydin Gol

Bibliographic Information

  • Book Title: Formal Methods for Discrete-Time Dynamical Systems

  • Authors: Calin Belta, Boyan Yordanov, Ebru Aydin Gol

  • Series Title: Studies in Systems, Decision and Control

  • DOI:

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-50762-0Published: 17 March 2017

  • Softcover ISBN: 978-3-319-84485-5Published: 21 July 2018

  • eBook ISBN: 978-3-319-50763-7Published: 08 March 2017

  • Series ISSN: 2198-4182

  • Series E-ISSN: 2198-4190

  • Edition Number: 1

  • Number of Pages: XVIII, 284

  • Number of Illustrations: 54 b/w illustrations, 39 illustrations in colour

  • Topics: Control and Systems Theory, Complexity, Systems Theory, Control

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