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.
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