A novel pinning observability strategy for Boolean networks

Observability is of biological and engineering significance for the study of large-scale Boolean networks (BNs), while sensors are commonly impossible or high-cost to be inflicted on all SVs. Taking an unobservable large-scale BNs into account, it is crucial to design an operably effective control strategy under which the controlled system achieves observability. In this paper, a novel pinning control strategy is developed for an unobservable BN. It takes advantage of the network structure (NS) with respect to (w.r.t.) $n$ SVs rather than the traditionary algebraic state space representation w.r.t. $2^n$ states. The application of NS information dramatically reduces the time complexity from $O(2^{2n})$ to $O(n2^{3\omega}+n^3)$, where $\omega$ and $p$ are respectively the largest out-degree of vertices and the number of senors. Moreover, the new approach is of benefit to identify the pinning nodes and concisely compute the corresponding feedback form for every pinning nodes. With regard to simulation, the T-LGL survival network with 18 SVs and T-cell receptor kinetics with 37 SVs and 3 input variables are investigated to demonstrate the availability of our theoretical results.