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Controlled timed Petri nets: equivalence relations, model reduction.

Boel, R.; Bordbar, B.; Stremersch, G.

In: Proc. IEEE Int. Conf. on Systems, Man, and Cybernetics (SMC'98), 11-14 October 1998, San Diego, CA, pages 674-679. 1998.

Abstract: This paper discusses controlled timed Petri net models for the formal synthesis of supervisory controllers for real time discrete event systems (e.g., communication protocols, supervisors for FMSs, control for batch processes). The standard Petri net formalism is extended with firing delays between the time a transition becomes state enabled, and the time it is executed. These firing delays are partly controllable between lower and upper bounds. The goal is to guarantee that certain forbidden distributions of tokens will never occur. The influencing net, corresponding to forbidden sets, is defined for this purpose. Deciding whether a maximally permissive controller exists, and if yes, constructing such a controller, requires solving large sets of linear inequalities over firing times in this influencing net. This is generally a very large set. Hence, some equivalence relations between different subnets of a timed Petri net can be helpful in reducing this set. An example shows that replacing a subnet by a simpler equivalent subnet can significantly reduce the size of the sets of inequalities to be solved.

Keywords: equivalence relations, model reduction, net equivalences, timed Petri nets.

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