Observability and reconstructibility of large-scale Boolean control networks via network aggregations

TL;DR

This paper introduces an aggregation method to efficiently verify observability and reconstructibility in large-scale Boolean control networks with special structures, reducing computational complexity and applicable to certain linear systems.

Contribution

It defines a special class of aggregations compatible with observability and reconstructibility, and proves conditions under which these properties hold for the entire network.

Findings

Aggregation reduces complexity in verifying properties.

Acyclic aggregations ensure properties of sub-networks imply the whole network.

Method demonstrated on a biological control system model.

Abstract

It is known that determining the observability and reconstructibility of Boolean control networks (BCNs) are both NP-hard in the number of nodes of BCNs. In this paper, we use the aggregation method to overcome the challenging complexity problem in verifying the observability and reconstructibility of large-scale BCNs with special structures in some sense. First, we define a special class of aggregations that are compatible with observability and reconstructibility (i.e, observability and reconstructibility are meaningful for each part of the aggregation), and show that even for this special class of aggregations, the whole BCN being observable/reconstructible does not imply the resulting sub-BCNs being observable/reconstructible, and vice versa. Second, for acyclic aggregations in this special class, we prove that all resulting sub-BCNs being observable/reconstructible implies the whole BCN being observable/reconstructible. Third, we show that finding such acyclic special aggregations with sufficiently small parts can tremendously reduce computational complexity. Finally, we use the BCN T-cell receptor kinetics model to illustrate the efficiency of these results. In addition, the special aggregation method characterized in this paper can also be used to deal with the observability/reconstructibility of large-scale linear (special classes of nonlinear) control systems with special network structures.