System Decomposition With Respect To Disturbances For Boolean Control Networks With Disturbances

Boolean networks are a kind of dynamic systems composed of logical variables and logical functions.Disturbed Boolean control networks are a kind of discrete dy-namic control systems with logic control variables and logical disturbances variables.Boolean networks have a good application background in genetic biology,which can be used to effectively analyze the interaction among genes.With the rapid develop-ment of systems biology,the issue of Boolean dynamic models has become a hotspot,which plays an important role in simulation and control of genetic regulation network-s.Since Boolean control networks have potential applications to the understanding and treatment of some genetic diseases,the control theory of Boolean control network-s has been paid great attention by the community of systems biology and community of control theory.Due to the introduction of the logical disturbance variables,some uncertainties of genetic regulation networks can be described.System decomposition with respect to disturbance for a Boolean control network with disturbance is to find a logical coordinate transformation such that the transformed system can be decom-posed into two subsystems,one of which is not affected by the disturbance.Solving the problem of system decomposition with respect to disturbance is very helpful to well understand the affect of the disturbance to the control systems.In this paper,Boolean control networks with disturbances are investigated by using algebraic and graph theory methods,and the problem of system decomposi-tion with respect to disturbances is proposed.Based on the algebraic representation of Boolean control networks,some equivalent conditions for the decomposability are ob-tained.Based on the concept of state transition diagram of a Boolean control network,a necessary and sufficient graphical condition for the decomposability is proposed.Finally,an algorithm of the decomposition is given.