Verification and Control of Hybrid Systems: A Symbolic Approach by Paulo Tabuada – A Springer Publication on Symbolic Mo

Introduction

In an era where software governs everything from automotive safety systems to medical devices, understanding the seamless interaction between digital computation and continuous physical processes has become essential. Verification and Control of Hybrid Systems: A Symbolic Approach by Paulo Tabuada offers a rigorous yet accessible pathway into this critical field. Published by Springer, this hardcover volume is an indispensable resource for researchers, graduate students, and practicing engineers who seek to master the verification and control of hybrid systems through symbolic methods.

Book Overview

Hybrid systems are at the heart of modern technology—they describe how discrete software models, such as finite-state machines, interact with continuous physical dynamics described by differential equations. This book systematically addresses two fundamental challenges: verification (ensuring the system behaves correctly) and controller synthesis (designing a controller that guarantees desired behaviour). While these problems are notoriously difficult for general hybrid systems, Professor Tabuada presents a groundbreaking symbolic approach that identifies classes of hybrid systems admitting finite or symbolic models. The text builds a coherent framework linking hybrid dynamics to symbolic representations, enabling powerful analysis and design techniques.

Key Highlights

• Systematic presentation of hybrid system classes that admit symbolic models, with clear relationships between the original system and its finite abstraction.
• Unified treatment of verification and controller synthesis, showing how symbolic models enable both tasks.
• Rigorous mathematical foundation combined with practical examples drawn from engineering applications.
• Self-contained exposition of key results for finite systems, making the book accessible even to readers new to the area.

Inside the Book

The book is structured to guide the reader from foundational concepts to advanced applications. Early chapters introduce hybrid systems and their modelling, followed by an in-depth exploration of symbolic models—including timed automata, o-minimal systems, and incremental stability. The middle sections delve into verification techniques, such as reachability analysis and temporal logic verification, while later chapters focus on controller synthesis using symbolic approaches. Numerous illustrative examples, including automotive and robotic systems, demonstrate the practical relevance of the methods discussed.

Key Topics

• Modelling of hybrid systems with differential equations and finite automata
• Symbolic models: timed automata, o-minimal hybrid systems, and approximately bisimilar systems
• Reachability analysis and safety verification
• Temporal logic verification for hybrid systems
• Controller synthesis using abstraction-based methods
• Relationships between hybrid dynamics and discrete abstractions

Reader Benefits

Readers will gain a deep understanding of how to transform complex hybrid systems into tractable symbolic models for verification and control. The book equips you with practical tools to analyse safety-critical systems, design robust controllers, and reason about system behaviour rigorously. By bridging theory and application, it helps you stay at the forefront of embedded systems research and development.

Learning Outcomes

• Understand the fundamental principles of hybrid systems and their symbolic representation
• Apply verification techniques to ensure correctness of hybrid control systems
• Design controllers using symbolic models and abstraction-based methods
• Identify classes of hybrid systems that admit finite abstractions
• Analyse real-world case studies in automotive, aerospace, and robotics domains

Who Should Read

This book is ideal for postgraduate students in control engineering, computer science, electrical engineering, and applied mathematics. It is also a valuable reference for researchers working in cyber-physical systems, embedded systems, and formal methods. Practising engineers involved in the design of safety-critical control systems will find the symbolic approach highly relevant to their work.

About the Author

Paulo Tabuada is a distinguished professor and researcher in the field of cyber-physical systems and control theory. He has made seminal contributions to the symbolic control of hybrid systems and is widely recognised for his ability to communicate complex mathematical ideas with clarity. His work bridges control theory, computer science, and formal verification, making him a leading authority in this interdisciplinary domain.

About the Publisher

Springer is a globally renowned academic publisher known for its high-quality scientific, technical, and medical books. With a legacy spanning over 180 years, Springer publishes cutting-edge research that shapes the future of engineering and science. This book is part of Springer's prestigious series on control engineering and computer science.

Conclusion

Verification and Control of Hybrid Systems: A Symbolic Approach is an essential addition to the library of anyone serious about understanding and designing hybrid systems. With its clear exposition, rigorous treatment, and practical examples, this book stands as a definitive guide to symbolic methods in verification and control. Order your hardcover copy today from Bookshops.in and take a decisive step toward mastering this transformative field.