State Estimation via Designing Controller and State Estimation-Based Stabilization for Boolean Control Networks

This article investigates the issues of state estimation and state estimation-based stabilization for Boolean control networks (BCNs). Unlike previous state observers, this article proposes an optimal state estimator by designing a particular input sequence for the first time, where the maximum-minimum method is employed such that the state of BCNs can be uniquely estimated in short time steps. A minimum reconstructible state set (MRSS) is constructed to determine this input sequence. Next, based on the estimated state, a finite-time stabilization scheme is proposed by constructing a switching controller consisting of three stages. A controller is first developed to estimate the state of BCNs in finite-time steps, and a state reachable controller is also provided to make the state of BCNs reachable to a given equilibrium point. Subsequently, a constant controller is further developed to stabilize the state of BCNs to the equilibrium point. Finally, an oxidative stress response model is used to illustrate the effectiveness of the proposed results.