Control of fuzzy cellular Automata: The case of rule 90

This paper is dedicated to the study of fuzzy rule 90 in relation with control theory. The dynamics and global evolution of fuzzy rules have been recently investigated and some interesting results have been obtained in [10,15,16]. The long term evolution of all 256 one-dimensional fuzzy cellular automata (FCA) has been determined using an analytical approach. We are interested in this paper in the FCA state at a given time and ask whether it can coincide with a desired state by controlling only the initial condition. We investigate two initial states consisting of a single control value u on a background of zeros and one seed adjacent to the controlled site in a background of zeros.