[ToC]

 

Anil Nerode and Wolf Kohn, "Models for Hybrid Systems: Automata, Topologies, Controllability, Observability," in Robert L. Grossman, Anil Nerode, Anders P. Ravn, Hans Rischel, eds., Hybrid Systems, Springer-Verlag, 1993

ANALOG WORLD | DIGITAL WORLD

Our second level of modelling models the control automaton in more detail. It is decomposed into a series of three successive units. The first unit is an analog to digital converter which converts each of an infinity of real number measurements into one of possibly finitely many symbols in the input alphabet of the "internal control automaton". (The internal control automaton, in practice, is a finite state automaton with finite input and finite output alphabets.) The second unit is the internal control automaton, which has as input a symbolic representation of a measurement and produces as output a symbolic representation of the next control law to be imposed on the plant and how long to apply it. The third unit is a digital to analog converter which converts these output symbols representing control laws and times into the actual control laws imposed on the plant.

These three subunits respectively represent: transition from the continuous to the digital; transition from digital to digital; and, finally, transition from digital to continuous. Figure 2 represents this.

When we substitute Figure 2 into Figure 1, we fet Figure 3. The digital world is represented below the lower heavy line. The analog world is represented above the upper heavy line. The interface between these two worlds consists of the converters and is represented between the heavy lines.