Hybrid Event Structures

We describe an event structure model in which issues related to continuous systems can be studied. The event structure model for hybrid system consists of a continuous component and a discrete component which interact with each other via the usual enabling and connict relations. The continuous components behave like communicating sequential agents. The discrete component can be viewed as a prime event structure. Towards modelling the simulation of hybrid systems, we derive discrete structures by sampling the continuous system. As a consequence of sampling, some information is lost while other information can be inferred from the sample. We focus on the concurrence of events and the innuence of sampling on it. We also present a few results related to the ability to infer the concurrence of events in sampled structures. 1 Motivation The term hybrid system denotes a discrete program interacting with an analog (or continuous) environment. This is a generalisation of the reactive model in which all components are discrete. Typical examples of hybrid systems include industrial plant control systems and aircraft control systems. Various models for hybrid systems have been proposed. The most common is that of real-time automata as deened by Alur and Dill 1] where time is the primary continuous component. More general forms of hybrid systems have been deened in Maler et al. 10] and in the volume devoted to hybrid systems edited by Grossman et al. 6]. Most of the models consist of a set of variables which can change continuously and a set of variables which can change discretely. A trace is then deened as a sequence of continuous changes separated by discrete changes. Such a behaviour is called a phase transition behaviour by Maler et al. 10]. By placing various restrictions on the continuously changing variables, specialised classes of hybrid systems such as linear hybrid systems, integrators and clocks can be deened. Benveniste et al. in 2] adopt a diierent approach. They assume a discrete sequence of values called signals which is augmented with a special value to indicate a lack of signal. There is no single global time, rather each sequence of signals can denote a logical clock (with lack of signal indicating no change in time.) The various components in the system are executed in a synchronous fashion i.e., there is a one to one correspondence between every sequence of signals. Based on boolean values and the presence or absence …