On Identification of Boolean Control Networks

TL;DR

This paper introduces a comprehensive analytical framework for identifying Boolean control networks, unifying existing methods under two phenomena, and provides criteria and algorithms for their identifiability and observability.

Contribution

It proposes a new systematic framework for BCN identification, unifies existing approaches, and establishes new criteria for identifiability and observability.

Findings

Observable BN is uniquely identifiable

O1-observable BCN is uniquely identifiable

Identifiable but not observable systems exist

Abstract

A new analytical framework consisting of two phenomena: single sample and multiple samples, is proposed to deal with the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the existing works on identification can be categorized as special cases of these two phenomena. Several effective criteria for determining the identifiability and the corresponding identification algorithms are proposed. Three important results are derived: (1) If a BN is observable, it is uniquely identifiable; (2) If a BCN is O1-observable, it is uniquely identifiable, where O1-observability is the most general form of the existing observability terms; (3) A BN or BCN may be identifiable, but not observable. In addition, remarks present some challenging future research and contain a preliminary attempt about how to identify unobservable systems.