  In this article, we design the distributed pinning controllers to globally
stabilize a Boolean network (BN), specially a sparsely connected large-scale
one, towards a preassigned subset of state space through the node-to-node
message exchange. Given an appointed state set, system nodes are partitioned
into two disjoint parts, which respectively gather the nodes whose states are
fixed or arbitrary with respect to the given state set. With such node
division, three parts of pinned nodes are selected and the state feedback
controllers are accordingly designed such that the resulting BN satisfies three
conditions: the states of the other nodes cannot affect the nodal dynamics of
fixed-state nodes, the subgraph of network structure induced by the fixed-state
nodes is acyclic, and the steady state of the subnetwork induced by the
fixed-state nodes lies in the state set given beforehand. If the BN after
control is acyclic, the stabilizing time is revealed to be no more than the
length of the longest path in the current network structure plus one. This
enables us to further design the pinning controllers with the constraint of
stabilizing time. Noting that the overall procedure runs in an exponentially
increasing time with respect to the largest number of functional variables in
the dynamics of pinned nodes, the sparsely-connected large-scale BNs can be
well addressed in a reasonable amount of time. Finally, we demonstrate the
applications of our theoretical results in a T-LGL survival signal network with
$29$ nodes and T-cell receptor signaling network with $90$ nodes.

Systems and Control;Systems and Control