Disturbance Decoupling of Probabilistic Boolean Networks
研究了概率布尔网络的干扰解耦问题，提出了两种解耦定义，利用代数表示和顶点划分方法给出了条件，并通过例子验证了结果。
This article addresses the disturbance decoupling problem (DDP) of probabilistic Boolean networks (PBNs). Existing research on the DDP of Boolean networks (BNs) has predominantly concentrated on deterministic BNs (DBNs), which inadequately model the complexities of real-world systems, particularly those exhibiting stochastic behavior and uncertainty. We introduce two definitions tailored to PBNs: disturbance decoupling in distribution and disturbance decoupling with probability one. Utilizing an algebraic representation framework, we derive algebraic conditions for both types of disturbance decoupling. Additionally, we employ a vertex partitioning approach to establish graphical conditions pertinent to these disturbance decoupling types. Our investigation further reveals the connections between DBNs and PBNs concerning disturbance decoupling. To demonstrate the effectiveness of our theoretical results, we present three examples.