A Faster Approach for Robust Set Stabilization of Boolean Control Networks

This paper presents new methods on robust set invariance, set stabilizability, and set stabilization of Boolean control networks (BCNs) subject to arbitrary disturbance inputs. We approach these problems from a novel algorithmic perspective and develop more efficient algorithms that scale to moderately large networks. The predecessor concept in graph theory is first generalized to a robust predecessor (RP) of a state set to handle nondeterministic state transitions. A direct connection between RPs and a robust control invariant set (RCIS) is established. After that, a simple recursive elimination algorithm is developed to identify the largest RCIS quickly. A faster method is then proposed to check robust set stabilizability and attain time-optimal robust set stabilization. Compared with existing methods, our algorithms feature lower time complexity and reduce the running time dramatically, as demonstrated by case studies for two biological networks.