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

Author:

Schafaschek Germano1,Hardouin Laurent2,Raisch Jörg1

Affiliation:

1. Fachgebiet Regelungssysteme , 26524 Technische Universität Berlin , Berlin , Germany

2. Laboratoire Angevin de Recherche en Ingénierie des Système , Université d’Angers , Angers , France

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.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Walter de Gruyter GmbH

Subject

Electrical and Electronic Engineering,Computer Science Applications,Control and Systems Engineering

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