Function Perturbation Impact on Feedback Stabilization of Boolean Control Networks

Function perturbation analysis of Boolean networks is an important topic in the study of gene regulation due to gene mutation or immeasurable variables. This brief studies the function perturbation impact on feedback stabilization of Boolean control networks (BCNs) by using the algebraic state space representation approach. First, the state feedback stabilization control design of BCNs is recalled and the function perturbation problem is formulated. Second, given a state feedback stabilizer, it is robust to the considered function perturbation if one of the following three cases happens: 1) the block where the function perturbation occurs is different from the block which is affected by the state feedback stabilizer (Case 1); 2) when Case 1 does not happen, the perturbed column converges to the equilibrium faster than the original column (Case 2); 3) when Cases 1 and 2 do not happen, the perturbed column does not belong to the reachable set of the original column (Case 3). Third, when the perturbed column belongs to the reachable set of the original column, a constructive procedure is proposed to modify the given state feedback stabilizer to be robust to the function perturbation. Finally, the obtained new results are applied to the function perturbation analysis of lactose operon in Escherichia coli. The main novelty of this brief is to develop a new theoretical framework for the robustness of feedback controllers of BCNs with respect to function perturbation, which is not solved in the existing literature.