On Modelling and Reasoning About Hybrid Systems

This paper concerns the development of formal approaches for specification, simulation and validation of real-time reactive systems. Most previous approaches to this problem have focussed on discrete systems wherein the behavior of the system is described as a sequence of discrete events or state changes; they do not provide a satisfactory solution for a wide range of hybrid systems whose behavior depends on discrete as well as continuous parameters. Several approaches have been proposed to model such hybrid systems, but they are not amenable to efficient simulation. We also show that these approaches cannot conveniently express a variety of triggering and preemption policies. We then present our approach to overcoming these problems, based on our model trace(h). Our approach is aimed at retaining the (relative) simplicity of discrete systems as far as possible, while still permitting descriptions of continuous behavior. Moreover, our approach can express many different triggering, enabling and preemption policies so as to conveniently model diverse hybrid systems. We also illustrate how simulation and mechanical reasoning can be accomplished for systems represented in trace(h). Trade-offs between expressive power and computational complexity are also discussed