On Fully Actuated Boolean Control Networks

This paper investigates fully-actuated general Boolean networks that can be equivalently transformed into algebraic representations by using the semi-tensor product of matrices. The study first establishes a set of necessary and sufficient conditions characterizing fully-actuated systems in this framework. The investigation further extends to subsystem decomposition analysis, revealing that the decomposability of fully-actuated subsystems can be equivalently characterized by the existence of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2^{s}$</tex>-complete partitions within the state transition graph of the considered BCN. This topological perspective establishes a crucial connection between algebraic properties and graph-theoretical features. To validate the theoretical advances, three examples are systematically presented, demonstrating the effectiveness of the proposed methodologies in both analytical and computational aspects.