Supervisory Control of Petri Nets with Language Specifications

In this chapter we discuss how Petri nets can be used in the framework of supervisory control theory. A discrete event system is defined in such a theory as a language generator: this motivates the need to start the chapter with a short but self-contained introduction to Petri net languages. We consider the monolithic supervisory design that requires to construct the concurrent composition of the plant with the specification, to check this structure for controllability and nonblockingness, and eventually to refine it. We show how Petri nets can be used within this approach and show that while the procedure can always be applied to bounded nets, in the case of unbounded Petri nets it may not be possible to obtain a Petri net supervisor. NOTE: A correction to the notion of ”uncontrollable marking” given in this paper as Definition 7, and a modified proof of Theorem 3 that takes into account the corrected notion, can be found in: B. Lacerda, P.U. Lima, ”On the Notion of Uncontrollable Marking in Supervisory Control of Petri Nets,” IEEE Trans. on Automatic Control, Vol. 59, No. 11, pp. 3069-3074, Nov. 2014. ∗Published as: A. Giua, Supervisory control of Petri nets with language specifications, in Control of DiscreteEvent Systems: Automata and Petri Net Perspectives, C. Seatzu, M. Silva, J.H. van Schuppen (Eds), Lecture Notes in Control and Information Science, Vol. 433, pp. 235-256, Springer, 2012.