On algorithms for state feedback stabilization of Boolean control networks

This paper deals with the algorithms for state feedback stabilization of Boolean control networks (BCNs). By resorting to the semi-tensor product (STP) technique, the labelled digraph that can be used to completely characterize the dynamics of BCNs is derived, which leads to an equivalent graphical description for the stabilization of BCNs. What is more interesting is the fact that the existence of a state feedback control law stabilizing the BCN to some given equilibrium point can be characterized in terms of its spanning in-tree. Consequently, two in-tree search algorithms, namely, the breadth-first search and the depth-first search, are proposed to design the state feedback stabilizing law when global stabilization is feasible. Besides, some basic properties about the tree-search algorithms are addressed. A biological example is employed to illustrate the applicability and usefulness of the developed algorithms.