Logical Foundations of Cyber-Physical Systems

About this Textbook

Cyber-physical systems (CPSs) combine cyber capabilities, such as computation or communication, with physical capabilities, such as motion or other physical processes. Cars, aircraft, and robots are prime examples, because they move physically in space in a way that is determined by discrete computerized control algorithms. Designing these algorithms is challenging due to their tight coupling with physical behavior, while it is vital that these algorithms be correct because we rely on them for safety-critical tasks.

This textbook teaches undergraduate students the core principles behind CPSs. It shows them how to develop models and controls; identify safety specifications and critical properties; understand abstraction and system architectures; design by invariant; reason rigorously about CPS models; verify CPS models of appropriate scale; and develop an intuition for operational effects.

The book is supported with detailed lecture notes, lecture videos, homework assignments, and lab assignments.

About the Author

The author is an Associate Professor in the Computer Science Department at Carnegie Mellon University. He develops the logical foundations of cyber-physical systems to characterize their fundamental principles and to determine how we can trust computers to control physical processes. He has a Ph.D. from the University of Oldenburg, Germany. He received an ACM Doctoral Dissertation Honorable Mention Award and NSF Career Award, and he was named one of the Brilliant 10 Young Scientists by the Popular Science magazine and one of AI's 10 to Watch by the IEEE Intelligent Systems Magazine.


"This excellent textbook marries design and analysis of cyber-physical systems with a logical and computational way of thinking. The presentation is exemplary for finding the right balance between rigorous mathematical formalization and illustrative case studies rooted in practical problems in system design."

(Rajeev Alur, University of Pennsylvania)

"[The author] has developed major important tools for the design and control of those cyber-physical systems that increasingly shape our lives. This book is a 'must' for computer scientists, engineers, and mathematicians designing cyber-physical systems."

(Anil Nerode, Cornell University)

"This book provides a wonderful introduction to cyber-physical systems, covering fundamental concepts from computer science and control theory from the perspective of formal logic. The theory is brought to life through many didactic examples, illustrations, and exercises. A wealth of background material is provided in the text and in an appendix for each chapter, which makes the book self-contained and accessible to university students of all levels."

(Goran Frehse, Université Grenoble Alpes)

Table of Contents

  1. Cyber-Physical Systems: Overview
Part I - Elementary Cyber-Physical Systems
  1. Differential Equations & Domains
  2. Choice & Control
  3. Safety & Contracts
  4. Dynamical Systems & Dynamic Axioms
  5. Truth & Proof
  6. Control Loops & Invariants
  7. Events & Responses
  8. Reactions & Delays
Part II - Differential Equations Analysis
  1. Differential Equations & Differential Invariants
  2. Differential Equations & Proofs
  3. Ghosts & Differential Ghosts
  4. Differential Invariants & Proof Theory
Part III - Adversarial Cyber-Physical Systems
  1. Hybrid Systems & Games
  2. Winning Strategies & Regions
  3. Winning & Proving Hybrid Games
  4. Game Proofs & Separations
Part IV - Comprehensive CPS Correctness
  1. Axioms & Uniform Substitutions
  2. Verified Models & Verified Runtime Validation
  3. Virtual Substitution & Real Equations
  4. Virtual Substitution & Real Arithmetic

Bibliographic Information

This textbook will soon appear with Springer.
  1. André Platzer.
    Logical Foundations of Cyber-Physical Systems.
    Springer, 2017. ISBN 978-3-319-63587-3.
    [bib | eprint | web]

Subject Index:
Mathematical Logic and Formal Languages