Toward a Boundary Regional Control Problem for Boolean Cellular Automata

An important question to be addressed regarding system control on a time interval $[0, T]$ is whether some particular target state in the configuration space is reachable from a given initial state. When the target of interest refers only to a portion of the spatial domain, we speak about regional analysis. Cellular Automata (CA) approach have been recently promoted for the study of control problems on spatially extended systems for which the classical approaches cannot be used. An interesting problem concerns the situation where the subregion of interest is not interior to the domain but a portion of its boundary. In this paper we address the problem of regional controllability of cellular automata via boundary actions, i.e., we investigate the characteristics of a cellular automaton so that it can be controlled inside a given region only acting on the value of sites at its boundaries.