Sensors Design for Large-Scale Boolean Networks via Pinning Observability

TL;DR

This paper introduces a novel sensor design method for large-scale Boolean networks using pinning observability, enabling efficient network observability through structural adjustments and reduced computational complexity.

Contribution

It presents a new pinning control-based approach for sensor construction that improves efficiency and scalability for large Boolean networks.

Findings

Reduced time complexity from exponential to polynomial in network size.

Successfully applied sensor design to biological networks.

Provides a practical framework for large-scale network observability.

Abstract

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 $O(n^2+n2^d)$, 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.