Controlling the Dynamics of the Fuzzy Cellular Automaton Rule 90, I.

Control problems on Cellular Automata (CA) models have been introduced in a rigorous mathematical framework [10]. In this paper, we attempt to apply the control theory concept to the special class of fuzzy CA for which more freedom is gained using a continuum state space. Focusing on the case of fuzzy rule 90, we investigate the possibility of finding a control u = (u(0), u(1), ..., u(T-1)) which forces the system at a localized cell, to achieve a given desired state at time T. The problem is studied starting from an initial configuration consisting of a single seed on a zero background.