Output Selection and Observer Design for Boolean Control Networks: A Sub-Optimal Polynomial-Complexity Algorithm

Abstract

Using a graph-theoretic approach, we derive a new sufficient condition for observability of a Boolean control network (BCN). Based on this condition, we describe two algorithms: the first selects a set of nodes so that observing this set makes the BCN observable. The second algorithm builds an observer for the observable BCN. Both algorithms are sub-optimal, as they are based on a sufficient but not necessary condition for observability. Yet their time-complexity is linear in the length of the description of the BCN, rendering them feasible for large-scale networks. We discuss how these results can be used to provide a sub-optimal yet polynomial-complexity algorithm for the minimal observability problem in BCNs. Some of the theoretical results are demonstrated using a BCN model of the core network regulating the mammalian cell cycle.