Reconstructing the State of a Boolean Control Network via State Feedback

The goal of this article is to investigate under what conditions a Boolean control network admits a state feedback control law that makes the resulting Boolean network reconstructible. Starting from an algebraic representation of the Boolean control network, we first propose a result that allows to significantly reduce the problem size, and hence to mitigate the curse of dimensionality that typically arises when dealing with logical systems of very large size. Subsequently, we provide a necessary and sufficient condition for the problem solvability that relies on the algebra of noncommutative polynomials. Finally, when such a condition holds, we present a procedure to design a possible state feedback controller that achieves the desired result.