Structural optimal control for safe Petri nets
Résumé
This article addresses the problem of forbidden states in both conservative and non-conservative safe Petri net (PN) models. The property of conservativeness is discussed, and its implications are analysed. The construction and formulation of control conditions in the context of safe and non-conservative PN models is investigated, emphasising the problem of control optimality. The fundamental issue studied is that of the equivalence between a forbidden state and its associated constraint. A new fashion of writing control conditions is proposed and used, in conjunction with the place-invariant synthesis method, for the generation of a control solution. The final controlled model obtained is a PN similar in size to the initial model. Finally, the approach is illustrated via a simple example.