Modifying Esterel Concepts to Model Hybrid Systems

Abstract

A hallmark of the Esterel language is the combination of perfect synchrony with total orthogonality and powerful constructs for preemption, suspension and trap handling. It is desirable to make this kind of expressiveness available for the description of hybrid systems, that is, systems whose evolution is understood in terms of segment-wise continuous functions over the real time axis. Our approach consists of modifying Esterel concepts, most notably by replacing the discrete time frame by a continuously advancing one. We are then able to state a semantics made up of transitions with closed execution intervals of non-zero length. By an instant we understand an execution interval within this framework. Hybrid signals may change their value during such an instant, non-hybrid ones, that is, classical signals immediately settle to a specific state and keep it the whole time. Time consumption still has to be specified explicitly, namely in that instants reflect jumps among control flow locations defined by pause statements; all other statements take no time in the sense that arbitrarily many of them may be sequentially executed regardless of the instant's duration. A transfer of perfect synchrony from the discrete to the continuous is in this way accomplished. We also consider an example, which is from the automotive domain, traces, bisimilarity and compositionality.