Continuization of Timed Petri Nets: From Performance Evaluation to Observation and Control

State explosion is a fundamental problem in the analysis and synthesis of discrete event systems. Continuous Petri nets can be seen as a relaxation of discrete models allowing more efficient (in some cases polynomial time) analysis and synthesis algorithms. Nevertheless computational costs can be reduced at the expense of the analyzability of some properties. Even more, some net systems do not allow any kind of continuization. The present work first considers these aspects and some of the alternative formalisms usable for continuous relaxations of discrete systems. Particular emphasis is done later on the presentation of some results concerning performance evaluation, parametric design and marking (i.e., state) observation and control. Even if a significant amount of results are available today for continuous net systems, many essential issues are still not solved. A list of some of these are given in the introduction as an invitation to work on them.