Abstract
In this paper we deal with the problem of controlling a safe place/transition net so as to avoid a set of forbidden markings \({\user1{\mathcal{F}}}\). We say that a given set of markings has property REACH if it is closed under the reachability operator. We assume that all transitions of the net are controllable and that the set of forbidden markings \({\user1{\mathcal{F}}}\) has the property REACH.
The technique of unfolding is used to design a maximally permissive supervisor to solve this control problem. The supervisor takes the form of a set of control places to be added to the unfolding of the original net.
The approach is also extended to the problem of preventing a larger set \({\user1{\mathcal{F}}}_{I}\) of impending forbidden marking. This is a superset of the forbidden markings that also includes all those markings from which—unless the supervisor blocks the plant—a marking in \({\user1{\mathcal{F}}}\) is inevitably reached in a finite number of steps.
Finally, we consider the particular case in which the control objective is that of designing a maximally permissive supervisor for deadlock avoidance and we show that in this particular case our procedure can be efficiently implemented by means of linear algebraic techniques.
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Submitted to Discrete Event Dynamic Systems. A preliminary version of this paper titled “Control of safe ordinary Petri nets with marking specifications using unfolding,” was published in the Proc. IFAC WODES'04: 7th Work. on Discrete Event Systems (Reims, France), September 2004. Contact author is Alessandro Giua.
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Giua, A., Xie, X. Control of Safe Ordinary Petri Nets Using Unfolding. Discrete Event Dyn Syst 15, 349–373 (2005). https://doi.org/10.1007/s10626-005-4057-z
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DOI: https://doi.org/10.1007/s10626-005-4057-z