Quantitative Models for Complex Physical Systems

Abstract

We present a quantitative model, called metric hybrid automata, for quantifying the behaviors of complex physical systems, such as chemical reaction control systems, manufacturing systems etc. Due to the introduction of a metric, the state space of hybrid automata forms a metric space, in which the difference of states can be quantified. Furthermore, in order to reveal the distance of system behaviors, we construct the simulation distance and the bisimulation distance, which quantify the similarity of system behaviors. Our model provides the basis for quantitative analysis for those complex physical systems.