Timed Continuous Petri Nets Research Articles

Optimal Model Predictive Control of Timed Continuous Petri Nets

This paper addresses the optimal control problem of timed continuous Petri nets under infinite servers semantics. In particular, our goal is to find a control input optimizing a certain cost function that permits the evolution from an initial marking (state) to a desired steady-state. The solution we propose is based on a particular discrete-time representation of the controlled continuous Petri net system, as a certain linear constrained system. An upper bound on the sample period is given in order to preserve important information of the timed continuous net, in particular the positiveness of the markings. The reachability space of the sampled system in relation to autonomous continuous Petri nets is also studied. Based on the resulting linear constrained model, the optimal control problem is studied through model predictive control (MPC). Implicit and explicit procedures are presented together with a comparison between the two schemes. Stability of the closed-loop system is also studied.

Observability of Timed Continuous Petri Nets: A Class of Hybrid Systems

Timed continuous Petri net systems with infinite server semantics are piecewise linear systems. This paper addresses several problems regarding the state observability of these systems. We assume that the initial marking/state is not known and measuring some places we want to estimate all the others. First, a study of the different linear systems corresponding to a continuous Petri net system is performed. It is shown that in some cases, some of them are redundant, and so can be disregarded. The notion of distinguishable configurations is introduced. It helps to give a necessary and sufficient criterion for the observability in infinitesimal time. Using results from linear structured systems (Commault et al. (2005)), the concept of generic observability is introduced and it is studied in the case of join free nets.