A Graph Theory Approach for Regional Controllability of Boolean Cellular Automata
For researchers in control theory and cellular automata, this work offers a novel graph-based framework for regional controllability, though its impact is limited to a specific class of systems.
This paper addresses regional controllability of Boolean cellular automata using boundary controls, providing necessary and sufficient conditions based on Hamiltonian circuits and strongly connected components via a graph theory approach. The controls are derived using a preimage method.
Controllability is one of the central concepts of modern control theory that allows a good understanding of a system's behaviour. It consists in constraining 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 models 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.