Pinning Stabilization of Logical Networks Based on Deformation of the State Transition Matrix

Boolean Networks (BNs) are a powerful model to describe how gene work and holistically interact with one another in system biology. Based on the requirement to guide the systems to a desired state, the stabilization problem becomes an important issue in BNs. Since the normal state feedback control puts controllers to all nodes, the control cost is relatively high. In this paper, we investigate the stabilization problem of BNs under pinning control strategy. Meanwhile, to cut down the cost of control to the most, the set of pinned nodes is minimized. Specifically, a four-procedure method as well as the corresponding computationally feasible algorithms are proposed to determine a minimum set of controlled nodes based on a deformed state transition matrix and a constructed digraph. Compared with the strategy traditionally based on the state transition matrix, the approach we proposed effectively reduces the computational complexity. Finally, gene networks are discussed as simulations, which demonstrate the effectiveness of the proposed method, minimizing the number of controlled nodes with lower time complexity.