Robust Set Stabilization of Boolean Control Networks: an Efficient Approach based on Reverse Set Propagation

This paper investigates the robust set stabilization of nondeterministic Boolean control networks (BCNs) subject to random disturbance inputs. Although this problem has been previously addressed in the literature, we propose an alternative approach primarily to decrease the computational complexity of the algorithms. Our technique is inspired by the set propagation technique in reachability analysis but is applied in reverse order, identifying all the layered sets of states that reach a target set in a specific order. Two algorithms are developed: the first determines the largest robust control invariant subset, while the second handles time-optimal robust set stabilization using the results from the first algorithm. In particular, all time-invariant state feedback gain matrices are identified. Our approach achieves the lowest computational complexity ever known, even lower than the current methods designed solely for deterministic set stabilization without any disturbances. Numerical simulations with two biological networks demonstrate the significantly reduced processing time of our algorithms. Overall, this study presents a new approach for robust set stabilization with improved efficiency, capable of handling relatively large BCNs beyond the capabilities of existing techniques.