On Boolean Control Networks -- an Algebraic Approach

Boolean network is a powerful tool in describing the genetic regulatory networks. Accompanying the development of systems biology, the analysis and control of Boolean networks have attracted much attention from biologists, physicists, and systems scientists. This paper surveys a series of recent results on Boolean (control) networks, obtained by the algebraic approach proposed by the authors. First, a brief introduction to the semi-tensor product of matrices and the matrix expression of logic is presented. Then the topological structure of Boolean networks is investigated. Finally, the basic control problems of Boolean control networks are explored, which include the controllability, observability, realization, stability and stabilization, disturbance decoupling, identification and optimization.