Minimum-time decentralized control of Choice-Free continuous Petri nets

This paper considers the problem of reaching a desired final state from a given initial one. Models are assumed to be Choice-Free continuous Petri nets. A minimum-time decentralized control scheme is proposed. The original system is cut into disconnected subsystems by a set of places (buffers). Local control laws (minimal firing count vectors) are first computed independently in subsystems, based on which the globally admissible ones are derived. In the process, two problems arise: (1) disconnected subsystems can exhibit different behaviors (firing sequences and consequently, the reachable markings) from the original ones, and (2) since the buffer places are essentially shared by more than one subsystem, there must be an agreement among the neighboring local controllers. The first problem can be overcome by complementing the disconnected subsystems with an abstraction of the parts that are missing. For this purpose, two reduction rules are proposed to substitute the missing parts by a set of places. For the second problem, a coordinator controller is introduced, and several algorithms are proposed to reach the agreement. The coordinator design is rather simple, because it does not need to know the detailed states and structures of subsystems. Finally, by applying an ON–OFF control strategy in each subsystem, the final state is ensured to be reached in minimum-time.