A General Control Framework for Boolean Networks

This paper focuses on making up for the drawback of recent results about pinning controllability of Boolean control networks (BCNs). First of all, a sufficient criterion is derived for the controllability of BCNs. Based on this criterion, to make an arbitrary BCN be controllable, an efficient method is developed to design the feasible pinning strategy which involves identifying pinning nodes and determining control form. Comparing with the traditional pinning approach of which time complexity is $O(2^{2n})$, the time complexity of this pinning method is reduced to $O(n2^{3\kappa}+(n+m)^2)$ with the number of state variables $n$, that of input variables $m$ and the largest in-degree among all nodes $\kappa$. Since a practical genetic network is always sparsely connected, $\kappa$ is far less than $n$ despite its size being large-scale. Finally, a T-cell receptor kinetics model with $37$ state nodes and $3$ input nodes is considered to demonstrate the application of obtained theoretical results.