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.

In this paper, a set of data is assumed to be obtained from an experiment that satisfies a Boolean dynamic process. For instance, the dataset can be obtained from the diagnosis of describing the diffusion process of cancer cells. With the observed datasets, several methods to construct the dynamic models for such Boolean networks are proposed. Instead of building the logical dynamics of a Boolean network directly, its algebraic form is constructed first and then is converted back to the logical form. Firstly, a general construction technique is proposed. To reduce the size of required data, the model with the known network graph is considered. Motivated by this, the least in-degree model is constructed that can reduce the size of required data set tremendously. Next, the uniform network is investigated. The number of required data points for identification of such networks is independent of the size of the network. Finally, some principles are proposed for dealing with data with errors.