A Hybrid Denotational Semantics for Hybrid Systems

In this article, we present a model and a denotational semantics for hybrid systems. Our model is designed so that it may be easily used for modeling large, existing embedded applications, which is a first step toward their validation. The discrete subsystem is modeled by a program written in an extension of an imperative language and the continuous subsystem is modeled by differential equations. We give a denotational semantics to the continuous system inspired by what is usually done for the semantics of computer programs and then we show how it merges into the semantics of the whole system. The semantics of the continuous system is computed as the fix-point of a modified Picard operator which increases the information content at each step. This fix-point is the supremum of a sequence of approximations and we show that this supremum exists and is the solution of a differential equation using Keye Martin’s measurement theory.