Synthetizing State Feedback Control Laws for Discrete Event Systems with Constrained Paths
Using Min-Plus Algebra

Nesrine BEN AFIA¹*, Said AMARI²
¹ LARATSI, National Engineering School of Monastir, 5019, Tunisia
nesrine.benafia@enim.u-monastir.tn (*Corresponding author)
² LURPA, Normal Superior School of Paris-Saclay, 91190, France
samari@ens-paris-saclay.fr

Abstract: This paper outlines a new algebraic method for controlling Timed Event Graphs to satisfy upper time bounds imposed on certain critical paths. Adequate conditions that pave the way for the existence of control laws in the form of state feedbacks have been established by relaxing and generalizing some previous works. The aim is to ensure compliance of these strict time constraints while keeping the main properties of the Timed Event Graphs such as liveness. The resulting control laws correspond to a set of added monitor places preventing the violation of time constraints. The theoretical results were applied to a manufacturing cell as a part of a flexible workshop exposed to strict time duration within some of its processes.

Keywords: Discrete Event Systems (DES), Timed Event Graphs (TEG), Min-Plus algebra, Temporal constraints, Control synthesis.

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CITE THIS PAPER AS:
Nesrine BEN AFIA, Said AMARI, Synthetizing State Feedback Control Laws for Discrete Event Systems with Constrained Paths Using Min-Plus Algebra, Studies in Informatics and Control, ISSN 1220-1766, vol. 30(1), pp. 39-52, 2021. https://doi.org/10.24846/v30i1y202104