A mathematical method for control problems on cellular automata models

The aim of this article is to promote cellular automata (CA) approach for studying control problems on spatially extended systems for which the classical approaches cannot be used. In a similar way as for distributed parameter systems (DPS), this article proposes a mathematical framework that presents CA as open systems with inputs and outputs. This should help to solve rigorously several problems which have been so far viewed in the context of CA approach but only from a computational point of view as observability, identification or control (A. Adamatzky, Identification of cellular Automata Taylor and Francis, 1994; S. El Yacoubi, A. El Jai and N. Ammor, Regional Controllability with Cellular Automata Models, Lecture Notes in Computer Sciences, Springer, 2002, pp. 357-367). The particular controllability problem is studied to illustrate how the proposed formalism could be easily applied. Some simulations for the additive case are given.