Formal Methods for Discrete-Time Dynamical Systems [Bookshelf

Abstract

Cyberphysical systems (CPSs) are the next generation of engineered systems that consist of several computing devices communicating with each other and interacting with the physical world via sensors and actuators. These complex systems are ubiquitous and can be found in automobiles, aircraft, and smart buildings. Researchers using formal methods have introduced notions of physicality into automata, called hybrid automata. The challenge with these techniques is verifying the discrete aspects of the hybrid systems, given the control system dynamics. This book is organized into three parts and one appendix. Part I, “Transition Systems, Automata, and Temporal Logics,” discusses the types of systems and specifications used throughout this book (Chapters 1 and 2). Part II, “Analysis and Control of Finite Transition Systems,” focuses on verification and control synthesis problems for finite transition systems from specifications as linear temporal logic (LTL) formulas (Chapters 3−5). Part III, “Analysis and Control of Discrete-Time Dynamical Systems,” introduces the computational frameworks for verification and control of (infinite) discrete-time dynamical systems from LTL specifications, which is the most extensive part of this book. This monograph gives a complete picture of formal methods for the two classes of discrete-time systems. It covers a wide range of advanced and fascinating topics from both computer science and control theory. This is a valuable textbook for beginners and/or experienced researchers from these two domains. Readers from computer science gain a brief introduction to control systems and further see how formal method ideas can be expanded to address these huge challenges. Meanwhile, readers with a control theory background gain a foundational introduction to specifying the system behavior in terms of temporal logic and learn how to connect their models to discrete models using bisimulation. This book is self contained and can be used in senior undergraduate-level and/or graduate-level courses. Furthermore, readers can pursue the relevant topics of interest using the bibliographical notes at the end of each chapter. Inevitably, there exist some editing typos and grammatical errors, as well as minor, insufficient descriptions. However, these errors do not hinder the book’s readability and understandability. Overall, this research monograph will serve as a fundamental and foundational introduction to this emerging and vibrant field.