Verifying Cyber-Physical Systems A Path to Safe Autonomy

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.

Sayan Mitra is Professor in the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign.

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