Efficient design of Petri-net supervisors with disjunctive specifications

M. V. Iordache and P. J. Antsaklis

In the Proceedings of the 2013 IEEE International Conference on Automation Science and Engineering, pp. 936--941, August 2013.

Abstract -- The supervision based on place invariants is an efficient method for the supervision of Petri nets in which each inequality constraint is implemented by one monitor place. However, this method assumes specifications that describe convex legal sets. Non-convex legal sets can be described by disjunctions of inequality constraints. Specifications consisting of disjunctions of inequality constraints are called here disjunctive specifications. Previous work has shown that under certain boundedness assumptions it is possible to implement supervisors enforcing disjunctive specifications with conventional Petri nets. However, in the worst case, the number of places of the least-restrictive supervisors was exponentially related to the size of the specification. This paper introduces an enhanced approach that generates supervisors in which the number of places is linearly related to the size of the specification. The generated supervisors are least restrictive and are implemented with conventional Petri nets. %The paper presents an approach for the design of supervisors for disjunctive constraints in which the supervisors are represented by labeled Petri nets. This approach extends our previous results in two ways. First, the supervisors are now guaranteed to be least restrictive. Second, the constraints may now also include the firing vector. The approach is illustrated on the readers/writers problem. While the results are obtained in the fully controllable and observable setting, issues arising when the system is partially controllable and partially observable are also discussed. The approach is developed under certain boundedness assumptions.

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