A hybrid relational modelling language

Abstract

Hybrid systems are usually composed by physical components with continuous variables and discrete control components where the system state evolves over time according to interacting laws of discrete and continuous dynamics. Combinations of computation and control can lead to very complicated system designs. We treat more explicit hybrid models by proposing a hybrid relational calculus, where both clock and signal are present to coordinate activities of parallel components of hybrid systems. This paper proposes a hybrid relational modelling language with a set of novel combinators which support complex combinations of both testing and signal reaction behaviours to model the physical world and its interaction with the control program. We provide a denotational semantics (based on the hybrid relational calculus) to the language, and explore healthiness conditions that deal with time and signal as well as the status of the program. A number of small examples are given throughout the paper to demonstrate the usage of the language and its semantics.