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

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Summary

Methods

Optimal control of timed event graphs with resource sharing and output-reference update.

Introduction
Preliminaries
Idempotent semirings
Semirings of formal power series
TEG models in idempotent semirings
Residuation theory
Optimal control of TEGs
Optimal control of TEGs with output-reference update
Modeling and optimal control of TEGs with resource sharing
Modeling of TEGs with one shared resource
Optimal control of TEGs with one shared resource
Modeling and optimal control of TEGs with multiple shared resources
Optimal control of TEGs with resource sharing and output-reference update
Problem formulation: the case of a single shared resource
Optimal update of the inputs: the case of a single shared resource
Extension to the case of multiple shared resources
Conclusion
Full Text
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