Maximally Permissive Control of Flexible Manufacturing Systems with Fewest Disjunctive Constraints
Résumé
For Petri net models whose legal reachability
spaces are non-convex, one cannot optimally control them by the
conjunctions of linear constraints. This work proposes a method
to find a set of linear constraints such that each constraint
can forbid all first-met bad markings and every legal marking
satisfies at least one constraint. Then, the disjunctions of the
obtained constraints can make all legal markings reachable
and forbid all first-met bad markings, i.e., the controlled net
is live and maximally permissive. The work also develops an
integer linear programming model to minimize the number of
the constraints. Finally, an example is provided to illustrate the
proposed method.