A graph theory approach for regional controllability of Boolean cellular automata

Sara Dridi; Samira El Yacoubi; Franco Bagnoli; Allyx Fontaine

A graph theory approach for regional controllability of Boolean cellular automata

Sara Dridi ^{1, 2} Samira El Yacoubi ^{3, 4, *} Franco Bagnoli ² Allyx Fontaine ⁵

* Corresponding author

1 UPVD - Université de Perpignan Via Domitia

2 Université de Florence

3 IMAGES-Espace DEV - Institut de Modélisation et d'Analyses en géo-environnement et santé - Espace Développement

UMR 228 Espace-Dev, Espace pour le développement

4 UMR 228 Espace-Dev, Espace pour le développement

5 UAG UFR SM - Université des Antilles et de la Guyane - UFR des sciences médicales

Abstract : Controllability is one of the central concepts of modern control theory that allows a good understanding of a system's behaviour. It consists in constraining a system to reach the desired state from an initial state within a given time interval. When the desired objective affects only a sub-region of the domain, the control is said to be regional. The purpose of this paper is to study a particular case of regional control using cellular automata models since they are spatially extended systems where spatial properties can be easily defined thanks to their intrinsic locality. We investigate the case of boundary controls on the target region using an original approach based on graph theory. Necessary and sufficient conditions are given based on the Hamiltonian circuit and strongly connected component. The controls are obtained using a preimage approach

Keywords : Regional controllability deterministic cellular automata graph theory Hamiltonian circuit strongly connected component

Document type :

Journal articles

Domain :

Computer Science [cs]

Complete list of metadatas

https://hal-univ-perp.archives-ouvertes.fr/hal-02142983
Contributor : Samira El Yacoubi <>
Submitted on : Wednesday, May 29, 2019 - 8:03:47 AM
Last modification on : Wednesday, September 4, 2019 - 5:26:02 PM

A graph theory approach for regional controllability of Boolean cellular automata

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A graph theory approach for regional controllability of Boolean cellular automata

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