Structural Controller for Logical Expression of Linear Constraints on Petri Nets

Based on the P-type composition of Petri nets (PNs) defined in this paper, a framework for a structural control of discrete event systems (DESs) is constructed such that a closed-loop PN is obtained by composing a plant PN and a controller. As for a disjunction or conjunctive normal form (CNF) of linear constraints, a new approach is proposed to design a structural controller in this framework. First, a switching-net is defined for a disjunction of constraints, and an extended plant is obtained through the P-type composition of a plant PN and switching-net. Second, the disjunction of bounded constraints is transformed into a conjunction of switching-constraints on the extended plant. Third, a controller is synthesized by designing monitors for conjunctive switching-constraints according to a supervision-based-on-place-invariant method. Fourth, in a similar manner, a controller is also designed for a CNF of bounded constraints. The resulting controller is maximally permissive if each disjunction of constraints meets the jump-free condition, and its size grows polynomially with the number of constraints. Another advantage is that the closed-loop system is still a PN for many real DES since a CNF can describe not only convex but also nonconvex state regions.