Verification and Control of Hybrid Systems

Hybrid systems describe the interaction of software, described by finite models such as finite-state machines, with the physical world, described by infinite models such as differential equations. This book addresses problems of verification and controller synthesis for hybrid systems. Although these problems are very difficult to solve for general hybrid systems, several authors have identified classes of hybrid systems that admit symbolic or finite models. The novelty of the book lies on the systematic presentation of these classes of hybrid systems along with the relationships between the hybrid systems and the corresponding symbolic models. To show how the existence of symbolic models can be used for verification and controller synthesis, the book also outlines several key results for the verification and controller design of finite systems. Several examples illustrate the different methods and techniques discussed in the book.

• approximate bisimulation
• approximate simulation
• bisimulation
• control synthesis
• simulation
• symbolic models
• system
• verification

From the reviews:

“The book covers a wide range of foundational topics in verification and control of hybrid systems. … The exposition is … smooth and readable. The author is undoubtedly an excellent writer. The book may be strongly recommended to researchers who want to understand the mathematical foundations of this field.” (I. Meznik, Mathematical Reviews, Issue 2010 h)

“The rapidly growing and interdisciplinary research demands that researchers must understand concepts and tools from both computer science and control theory. This is undoubtedly a daunting task, and this is where this book can come to the rescue. It covers a wide range of   foundational topics in verification and control of hybrid systems. … This book will be useful for researchers, engineers, computer scientists, and graduate students in the areas of formal methods, verification, model checking, and control.” (Alexander O. Ignatyev, Zentralblatt MATH, Vol. 1195, 2010)

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