Abstract
Abstract Timed event graphs (TEGs) are a subclass of timed Petri nets that model synchronization and delay phenomena, but not conflict or choice. We consider a scenario where a number of TEGs share one or several resources and are subject to changes in their output-reference signals. Because of resource sharing, the resulting overall discrete event system is not a TEG. We propose a formal method to determine the optimal control input for such systems, where optimality is in the sense of the widely adopted just-in-time criterion. Our approach is based on a prespecified priority policy for the TEG components of the overall system. It builds on existing control theory for TEGs, which exploits the fact that, in a suitable mathematical framework (idempotent semirings such as the max-plus or the min-plus algebra), the temporal evolution of TEGs can be described by a set of linear time-invariant equations.
Highlights
In this paper, we consider a scenario where several discrete event subsystems, each modeled by a timed event graph (TEG), share one or more resources and where the reference signals for the subsystems may change unexpectedly
It builds on existing control theory for TEGs, which exploits the fact that, in a suitable mathematical framework, the temporal evolution of TEGs can be described by a set of linear timeinvariant equations
We consider a scenario where several discrete event subsystems, each modeled by a timed event graph (TEG), share one or more resources and where the reference signals for the subsystems may change unexpectedly
Summary
Optimal control of timed event graphs with resource sharing and output-reference update.
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