Verifying Cyber-Physical Systems

A graduate-level textbook that presents a unified mathematical framework for modeling and analyzing cyber-physical systems, with a strong focus on verification.

Verification aims to establish whether a system meets a set of requirements. For such cyber-physical systems as driverless cars, autonomous spacecraft, and air-traffic management systems, verification is key to building safe systems with high levels of assurance. This graduate-level textbook presents a unified mathematical framework for modeling and analyzing cyber-physical systems, with a strong focus on verification. It distills the ideas and algorithms that have emerged from more than three decades of research and have led to the creation of industrial-scale modeling and verification techniques for cyber-physical systems.Preface xv
1 Introduction 1
2 Modeling Computation 17
3 Modeling Physics 31
4 Modeling Cyber-Physical Systems 55
5 Composing Models 79
6 Specifying Requirements 101
7 Verifying Invariants 123
8 Abstractions and Compositional Reasoning 145
9 Reachability Analysis 165
10 Progress Analysis 197
11 Data-Driven Verification 217
Appendix A: Linear Algebra and Real Analysis 247
Appendix B: Computability and Complexity 255
Appendix C: Specification Language Reference 263
References 271
Index 291“Mitra’s book provides a thoroughly modern view of the techniques for specification and verification of cyber-physical systems, expertly explaining how tools from control theory, dynamical systems, automata theory, and formal methods can be combined to analyze safety in autonomous systems. Using a combination of conceptual examples that can be used to understand basic concepts and modern applications that motivate the need for new approaches, this book provides the foundation for practitioners interested in understanding conceptual frameworks for verification of hybrid systems and researchers interested in establishing a rigorous basis for further advances.”
—Richard Murray, Thomas E. and Doris Everhart Professor of Control and Dynamical Systems and Bioengineering, Caltech
 
“This is an excellent textbook that gives a comprehensive introduction to state-of-the-art techniques in formal modeling and verification of cyber-physical systems. Its seamless integration of technical details and illustrative examples makes it ideally suited for graduate students hoping to understand this complex subject matter.”
—Rajeev Alur, Zisman Family Professor in the Department of Computer and Information Science, University of PennsylvaniaSayan Mitra is Professor in the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign.: A graduate-level textbook that presents a unified mathematical framework for modeling and analyzing cyber-physical systems, with a strong focus on verificati