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## A min-plus polynomial approach to forbidden state control for general Petri nets.

Boel, R.K.;
Bordbar, B.;
Stremersch, G.
In:
*Proceedings of the 4th International Workshop on Discrete Event Systems*, pages 79-84.
August 1998.

Abstract:
This paper treats feedback control design for discrete event systems,
modeled as Petri nets, with avoidance of forbidden states as specification
of the control goal. It has been shown before that for calculating
maximally permissive feedback controls attention can be limited to the
marking of a subnet, the influencing net. We first show that the
influencing net can be described algorithmically using min-plus algebra.
Next we introduce a general approach for calculating state feedback
controls by decomposing the set of places and the set of transitions in
the uncontrolled net in a number of layers. These layers are used to
construct a min-plus polynomial which has to be maximized to obtain the
maximal value of the expressions specifying the control goal. An example
shows that in many interesting cases it is possible to eliminate most of
the variables, allowing efficient control design for general Petri net
models.

Keywords:
Petri net, supervisory control, min-plus algebra, influencing net.

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