Hybrid modelling of continuous-variable systems with application to supervisory control

The paper concerns supervisory control tasks in which a continuous system has to be moved into a globally defined final state. A hybrid model is proposed that describes the discrete-event behaviour as well as the quantitative behaviour of the continuous-variable system. The model consists of a Petri net and of differential equations whose validity depends on the marking of the net. The supervisory control task is solved by searching for a path within the Petri net from the current towards the final state and by using the relevant quantitative models to determine the speed of the state transitions. The results are illustrated by means of a laboratory tank system.