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A control method for distributed continuous mono-T-semiflow Petri nets†

A distributed continuous Petri net system (DCPN) is composed of several subsystems that are interconnected through buffers that are origin and destination private (i.e. modelled by places such that its input transitions belong to only one subsystem and its output transitions also belong to only one subsystem). In this framework, the control problem of driving a DCPN from an initial state to a target one is considered. Such a control problem can be divided into two tasks: (1) computation of a firing count vector that ensures the reachability of the target marking in the untimed subsystem; (2) implementation of a local control law executing the computed firing count vector in every timed subsystem. This work mainly focuses on the first task, which is achieved by the network of interconnected local coordinators located at subsystems. In particular, the firing count vectors are obtained as a result of a negotiation among those local coordinators. A distributed algorithm that implements the negotiation performed by each coordinator is presented and it is formally proved that the subsystems reach the target marking.