# Verification and Control of Hybrid Systems: A Symbolic Approach

Verification and Control of Hybrid Systems: A Symbolic Approach

With a foreword by Rajeev Alur

Paulo Tabuada

Springer 2009

ISBN: 978-1-4419-0223-8

Hybrid systems describe the interaction of software, modeled by finite-state systems such as finite-state machines, with the physical world, described by infinite-state systems such as differential equations. * Verification and Control of Hybrid Systems* provides a unique systematic exposition of several classes of hybrid systems, admitting symbolic models along with the relationships between them. The text outlines several key verification and control synthesis results for hybrid systems, guided by the concept of bisimulation, and illustrated by numerous examples.

The book is divided into four parts:

Part I presents basic concepts centered on a notion of system that is general enough to describe finite-state, infinite-state, and hybrid systems.

Part II discusses the ways in which systems relate to other systems, such as behavioral inclusion/equivalence and simulation/bisimulation, using these relationships to study verification and control synthesis problems for finite-state systems.

Part III draws inspiration from timed automata to present several classes of hybrid systems, with richer continuous dynamics, that can be related to finite-state symbolic systems. Once such relationships are established, verification and control synthesis problems for these hybrid systems can be immediately solved by resorting to the techniques described in Part II for finite-state systems.

Part IV follows the same strategy by generalizing simulation/bisimulation relationships to approximate simulation/bisimulation relationships that can be used for a wider class of hybrid systems.

This comprehensive treatment will appeal to researchers, engineers, computer scientists, and graduate students in the areas of formal methods, verification, model checking, and control and will undoubtedly inspire further study of the specialized literature.

*A list of typos, corrections, and additional material will be posted on this page.*

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