Some Control and Observation Issues in Cellular Automata

Abstract

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.

Observability and reconstructibility of bounded cellular automata

“…The observability and reconstructibility problem of cellular automata is only very little studied (El Yacoubi, 2008;El Yacoubi et al, 2021). However, bounded cellular automata can be seen as a special case of boolean networks which, on the other hand, are widely studied.…”

Synchronisation of Elementary Cellular Automata with a Small Initial Error. Application to Rule 18

“…This state estimation problem is widely studied by classical control theory [5,7] and it follows from the verification of observability, a notion that ensures that the sensors are well placed. This notion of observability can be applied to cellular automata (CA) [4,6,3] (and by extension to Boolean networks [10] which can be seen as a generalization of CA) but its evaluation has proven to be extremely complicated when it comes to non-linear CA [6].…”