Sensors Design for Large-Scale Boolean Networks via Pinning Observability

In this paper, a set of sensors is constructed via the pinning observability approach with the help of observability criteria given in [1] and [2], in order to make the given Boolean network (BN) be observable. Given the assumption that system states can be accessible, an efficient pinning control scheme is developed to generate an observable BN by adjusting the network structure rather than just to check system observability. Accordingly, the sensors are constructed, of which the form is consistent with that of state feedback controllers in the designed pinning control. Since this pinning control approach only utilizes node-to-node message communication instead of global state space information, the time complexity is dramatically reduced from $O(2^{2n})$ to $O(n^2+n2d)$, where where $n$ and $d$ are respectively the node number of the considered BN and the largest in-degree of vertices in its network structure. Finally, we design the sensors for the reduced D. melanogaster segmentation polarity gene network and the T-cell receptor kinetics, respectively.