Algorithm

Control (management)

Engineering

Discrete mathematics

Boolean function

Materials science

Node (physics)

Theoretical computer science

Dimension (graph theory)

Computer science

Matrix (chemical analysis)

Mathematics

Notation

Boolean network

Artificial intelligence

Composite material

Combinatorics

Structural engineering

State (computer science)

Arithmetic

IEEE Transactions on Control of Network Systems

Boolean networks (BNs) are discrete-time systems, where nodes are interconnected (here, we call such connection rule among nodes as a network structure), and the dynamics of each gene node is determined by logical functions. In this article, we propose a new approach on pinning control design for global stabilization of BNs based on BNs&#x2019; network structure, named as network-structure-based distributed pinning control. Compared with the existing literature, the design of pinning control is not based on the state transition matrix of BNs. Hence, the computational complexity in this article is reduced from <inline-formula><tex-math notation="LaTeX">$O(2^{2n})$</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">$O(n^2+n2^K)$</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of nodes and <inline-formula><tex-math notation="LaTeX">$K\leq n$</tex-math></inline-formula> is the largest number of in-neighbors of nodes. In addition, without using the state transition matrix, global state information is no longer needed; the design of pinning control is just based on neighbors&#x2019; local information, which is easier to implement. The proposed method is well demonstrated by several biological networks with different sizes. The results are shown to be simple and concise, while the traditional pinning control cannot be applied for BNs with such a large dimension.

A New Approach to Pinning Control of Boolean Networks