Denotational Semantics of Hybrid Automata

A hybrid automaton [16,2] is a digital, real-time system that interacts with an analogue environment. Hybrid automata are ubiquitous in all areas of modern engineering and technology. For example, the (digital) height control of an automobile chassis depends on and influences the (continuous) driving conditions of the vehicle [22]. Hybrid automata typically operate in safety critical areas, such as the highway control systems [25,21] and air traffic control [24]. They combine a finite set of control states with continuous dynamics. In every control state, the continuous variables evolve according to an ordinary differential equation (or, more generally, differential inclusion [4]), and the system changes control states if the continuous variables reach certain thresholds; every such state change can involve non-continuous re-assignment of the continuous variables.