Application and Theory of Petri Nets and Concurrency

In this lecture we first introduce supervisory control theory for discrete-event systems (DES) in a framework of finite automata and regular languages, with emphasis on the criteria of nonblocking and maximal permissiveness. Also stressed is the importance of control modularity and transparency. Turning to Petri Nets (PN), we indicate how the counterpart control design problem can be posed and (in many but not all cases) solved using integer linear programming. Finally we discuss the feasibility of a “DES transform” approach by which the PN problem is first converted to a DES problem, and the DES solution converted back to a PN implementation. Here we point out several interesting issues for further research.

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