Estimation Problems Of Gene Regulatory Networks With Special Structures

With the success of Mendel's hybrid pea experiment,the discovery of DNA structure and the initiation of human genome sequencing,genetic regulatory networks have developed rapidly.Among the biological networks,genetic regulatory networks are the most widely used ones.Genetic regulatory networks study the interrelationship between genes,mainly summarized as the interaction between mRNAs and proteins in genes.Genetic regulatory network is a complex biological nonlinear dynamic system that describes the interactions in gene expression.In this thesis,we study the state estimation of genetic regulatory networks with specific structures.The main content is as follows:First,the state estimation problem of time-delay coupled recurrent genetic regulatory networks is investigated.The coupled network consists of two recurrent sub-networks,which directly inhibit each other.By constructing a suitable Lyapunov-Krasovski functional(LKF),the delay-dependent stability criterion of the error system is given in the form of a linear matrix inequality.Then,the state observer of the considered genetic regulatory network is obtained.Finally,a numerical example is given to illustrate the validity of the theoretical results.Second,the state estimation problem of a time-delay genetic regulatory network with two coupled central modes is considered.The coupled network consists of two central sub-networks that directly promote or inhibit each other.The goal is to estimate the states of system by means of measurable outputs.The LKF associated with the structural features of genetic regulatory network is constructed,and the delay-dependent asymptotic stability criterion for the error system is investigated.It is described in the form of a linear matrix inequality.Then,the state observer of the studied genetic regulatory network is obtained.Finally,a numerical example is given to verify the validity of the designed state observer.Finally,the state estimation problem of coupled recurrent-central structural genetic regulatory networks with a constant delay is investigated.The coupled network consists of a cyclic subnetwork and a central subnetwork,which promote or inhibit each other.The goal is to estimate the states by the measured outputs.A sufficient condition for the global exponential stability of the error system is obtained by the definitions of the global exponential stability and the Moore–Penrose inverse of matrix.Then,the state observer of the studied genetic regulation network is designed.Finally,a numerical example is given to verify the validity of the designed state observer.The novelties of this paper includes:(1)fill the gap in the design of state observers for time-delay genetic regulatory networks with coupled special structures;(2)describe the exact form of the observers based on feasible solutions of linear matrix inequalities;(3)A new method to fit LFK of the model characteristics is proposed,which overcomes the difficulty of finding suitable LKFs.