Study On Controllability And Observability Of Two Types Of Discrete Boolean Network System

As a kind of discrete time dynamic evolution system of binary logic,Boolean network has the function of simulating cell differentiation and gene regulation of organisms,and has been widely used in biology and systems science.This thesis mainly studies two kinds of problems: one is the solvability and controllability of discrete linear systems in the sense of Boolean control network.The second is the observability of Markovian jump Boolean network with random time delay.Firstly,the logical equation of Boolean network is transformed into a discrete time linear system by the left half tensor product of matrix.For the transformed discrete linear system,the expression of the exact solution is derived.By means of the improved definition of controllability,the algebraic expression containing state reachable sequences is given,and then the sufficient and necessary condition for the controllability of the system is given.Secondly,for Markovian jump Boolean network with random time delay,the observability is transformed into the accessibility among state subsets of the extended system by using parallel extension technique,and the corresponding simplified dynamical system is given by means of distinguishable subsets and presupposed indication matrix,and the accessibility among state subsets is transformed into the stability of the simplified dynamical system.Based on the theory of non-negative dynamical system,the sufficient and necessary condition for judging observability of the system is given.Finally,the validity of the theoretical results is verified by examples of biology and logic.