Stabilization of Boolean Networks: A Model-Free Constrained State-Flipped Control Approach

In this paper, we explore the stabilization of Boolean Networks (BNs) under state-flipped control, incorporating three key constraints to address the challenges of disease treatment response times and the practical limitations of therapeutic interventions. Our approach includes: (i) a feasible flipped nodes constraint to ensure a subset of nodes can be realistically manipulated; (ii) a transient period constraint to align treatment with time-sensitive windows of therapeutic opportunity; and (iii) a constraint on the number of flip transitions to minimize resource consumption and potential side effects. Furthermore, an evolution selection rule is set for the BNs. Then, a necessary and sufficient condition is given for the stabilization under the above constraints. We present a modified Q-learning (QL) algorithm to design a policy for stabilization under constraints in the model-free case. Finally, BN models of metastatic melanoma network and T-cell large granular lymphocyte (T-LGL) network are considered to show the applicability of our results.