Controlling the Dynamics of FCA Rule 90 in [0, 1]T
Samira Elyacoubi and Angelo B. Mingarelli
We consider one-dimensional Fuzzy Cellular Automata (FCA) defined as a real-valued version of elementary cellular automata (ECA) i.e., the cells are identified with the real values in [0, 1] rather than the binary ones. We analyse possible ways of controlling the FCA dynamics in order to find a signal u = (u0, u1, . . . , uT−1) which forces the system to reach at a horizon time T > 0, some particular target states starting from a specific initial condition. The control components ui, i = 0, . . . , T − 1 which excite the system at time i are also taken in [0, 1]. The admissible controls are then to be found in [0, 1]T. This case is conceptually more difficult than our previous work dedicated to solve the same control problem in RT. We investigate the particular FCA rule 90 in the case of a single seed on a zero background. We prove the existence of such a control for small values of T and show that generically, the larger the value of T the “smaller” the set of admissible controls.
Keywords: cellular automata, fuzzy rules, control theory