Verification and Control of Hybrid Systems

This book examines several classes of hybrid systems, admitting symbolic models along with the relationships between them. It outlines several key verification and control synthesis results for 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.

Unified presentation of different abstraction techniques for hybrid systems Unified treatment of the notions of simulation and bisimulation across discrete, continuous and hybrid systems Thorough discussion of the recently introduced notions of approximate simulation and bisimulation for continuous and hybrid systems Illustration of the concepts through examples Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt
Basic concepts.- Systems.- Verifcation problems.- Control problems.- Finite systems.- Exact system relationships.- Verification.- Control.- Infinite Systems Exact symbolic models.- Exact symbolic models for verification.- Exact symbolic models for control.- Infinite Systems Approximate symbolic models.- Approximate system relationships.- Approximate symbolic models for verification.- Approximate symbolic models for control.