Modeling Time in Hybrid Systems: How Fast Is "Instantaneous"?

Many of today's electro-mechanical devices exhibit both continuous and discrete behavior. Modeling these hybrid systems presents special challenges for automated modeling and simulation. We show how nonstandard analysis overcomes these challenges, provides a firm mathematical foundation, and satisfies our intuitions about the behavior of hybrid systems. 1 Introduction Many of today's electro-mechanical devices exhibit both continuous and discrete behavior. Modeling these hybrid systems presents special challenges for automated modeling and simulation. Work in discrete event simulation [2] assumes that all change is discrete; work in quantitative and qualitative simulation assumes that all change is (at least piecewise) continuous. The behavior of hybrid systems, such as digitally controlled copiers, chemical plants, automobiles, etc., is not appropriately characterized as either continuous or discrete. A hybrid model of a system is almost always the result of an abstraction that simpl..