Robust control invariance of probabilistic boolean control networks via state‐flipped control

Abstract Robust control invariance (RCI) is crucial for ensuring that the state of the system remains within the predefined set under disturbances. In this paper, we study the robust control invariance issues of probabilistic Boolean control networks using state‐flipped control (SFC). Employing the semi‐tensor product method, we propose a matrix‐based testing condition to determine whether a given set can become a robust SFC invariance set under a specified SFC scheme. Additionally, we derive a necessary and sufficient condition to test the existence of feasible SFC schemes. To optimize the process, we present an algorithm that calculates feasible SFC schemes with the minimal flip set, ensuring the given set becomes a robust SFC invariance set. The idea of the algorithm is to identify all beneficial states for achieving RCI and direct the system towards these states, thereby avoiding the need to explore all possible SFC schemes and significantly reducing time complexity. Compared with the event‐triggered approach, our method reduces the time complexity of designing feasible control schemes from to . Finally, a biological simulation is presented to demonstrate the effectiveness of the theoretical results.