On the enforcement of a class of constraint in Petri nets

This paper addresses the enforcement of a class of linear inequality constraint defined on the marking of a Petri net (PN). The constraint may be regarded as the conjunction of ´less-than-or-equal-to´ inequality and ´greater-than-or-equal-to´ inequality. The extended Petri nets such as inhibitor arc PN and its complementary net, the so-called enabling arc PN, are exploited to design a PN supervisor such that the constraint is enforced in the controlled net. The supervisor is optimal in the sense that it allows the net evolves with least restriction while the given constraint is satisfied. An example is provided for illustration.