Complex Systems

Some Control and Observation Issues in Cellular Automata Download PDF

Samira El Yacoubi
Théo Plénet

IMAGES-ESPACE-DEV, Univ. Perpignan Via Domitia, Perpignan, France
ESPACE-DEV, Univ. Montpellier, IRD, Montpellier, France

Sara Dridi
University of Setif, Setif, Algeria
Franco Bagnoli
Dept. Physics and Astronomy and CSDC, University of Florence
via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy also INFN, sez. Firenze

Laurent Lefèvre
Clément Raïevsky

Univ. Grenoble Alpes, Grenoble INP, Institute of Engineering Univ. Grenoble Alpes, LCIS, 26000 Valence, France


This review article focuses on studying problems of observability and controllability of cellular automata (CAs) considered in the context of control theory, an important feature of which is the adoption of a state-space model. Our work first consists in generalizing the obtained results to systems described by CAs considered as the discrete counterpart of partial differential equations, and in exploring possible approaches to prove controllability and observability. After having introduced the notion of control and observation in cellular automata models, in a similar way to the case of discrete-time distributed parameter systems, we investigate these key concepts of control theory in the case of complex systems. For the controllability issue, the Boolean class is particularly studied and applied to the regional case, while the observability is approached in the general case and related to the reconstructibility problem for linear or nonlinear CAs.

Keywords: cellular automata; control systems; controllability; observability

Cite this publication as:
S. El Yacoubi, T. Plénet, S. Dridi, F. Bagnoli, L. Lefèvre and C. Raïevsky, “Some Control and Observation Issues in Cellular Automata,” Complex Systems, 30(3), 2021 pp. 391–413.