Observability And Fault Detection Of Boolean Control Networks

The modeling and analysis of gene regulatory networks is an important research topic in systems biology.Kauffman first proposed Boolean networks to simulate gene regulatory networks in 1969.Boolean networks are very suitable for modeling gene regulatory networks,which attracts much attention of many experts and scholars.In this paper,systematic analysis on Boolean networks using semi-tensor product method will be studied to better understand and model gene regulatory networks.The main contents of this paper are as follows:Chapter 1 introduces the research background and preliminaries knowledge of this paper,including the definition and properties of semi-tensor product of matrices,the matrix representation of logic functions and the algebraic expression of Boolean networks.Chapter 2 studies the minimum observability of Boolean control networks.Firstly,a new system is constructed by using Boolean control networks to analyze the dynamic trajectories of state sequence pairs.On this basis,one necessary and sufficient criterion for the observability of the Boolean control networks is obtained.Secondly,the new observers are added to improve the observability of the system without affecting observability.Then an observer design algorithm is given.In addition,a necessary condition for determining the minimum number of nodes is obtained,and an algorithm for solving the minimum observability problem is proposed.Finally,an example is given to illustrate the effectiveness of the results.Chapter 3 studies the problem of fault detection in Boolean networks.Firstly,one algorithm to determine locations of fault is given.Then,a pinning control method is designed for faulty Boolean networks to achieve global stabilization,while reducing the impact of faults.Finally,an example is given to illustrate the effectiveness of the obtained theoretical.