On just-in-time control of timed event graphs with input constraints: a semimodule approach
Timed event graph (TEG) is a subclass of timed Petri nets that can be used to model discrete event systems subject to synchronization and time delay phenomena. Just-in-Time control in TEG can be defined as the determination of latest admission date of resources in order to respect a given demand profile. In this paper this kind of control problem is studied in situations in which the input dynamics are constrained to a given semimodule (a kind of linear vector space in a semiring context). We give necessary and sufficient conditions to solve the problem and present two computational methods to solve it. Application examples are presented to illustrate the applicability of the results.
KeywordsTimed petri nets Max-plus algebra Residuation theory Semimodule Just-in-time control
The authors are grateful Brazilian agencies CAPES, CNPq and FAPEMIG for the financial support.
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