A graph theory approach for regional controllability of Boolean cellular automata

Controllability is one of the central concepts of modern control theory that allows a good understanding of a system’s behaviour. It consists in con- straining a system to reach the desired state from an initial state within a given time interval. When the desired objective affects only a sub-region of the domain, the control is said to be regional. The purpose of this paper is to study a particular case of regional control using cellular automata mod- els since they are spatially extended systems where spatial properties can be easily defined thanks to their intrinsic locality. We investigate the case of boundary controls on the target region using an original approach based on graph theory. Necessary and sufficient conditions are given based on the Hamiltonian circuit and strongly connected component. The controls are obtained using a preimage approach.