| Learning and modeling genetic regulatory networks are an important problem in systems biology.Boolean networks(BNs),which were firstly introduced by Kauffman in 1969,have been successfully used to characterize genetic regulatory networks.Ac-cording to the actual environment,several complex gene regulating networks can be described as BNs in which each gene is regarded as a vertex of the network and inter-acted with each other.Up to now,many fundamental works have been presented for the dynamics of the BNs,which plays a significant role in exploring the mechanism of life activities and treatment of disease.In BNs,each gene expression is quantized into two levels(ON:1 or OFF:0),at each discrete time t=0,1,2,...,then every gene has itself states at t + 1 that are determined by the states of its neighboring genes at t via certain logical rules.Therefore,BNs are discrete-time logical systems.However,it is quite difficult to analyze the large-scale gene regulating network because of the lack of suitable tools.In this paper,by the semi-tensor product(STP)method,discrete-time logical systems can be converted into discrete-time linear systems,which facilitates the analysis of BNs.To be concrete,the contributions of this dissertation are as follows:The definition and properties of STP are given in chapter one,including the algebraic expressions of logical functions and BNs.The chapter two investigates disturbance decoupling problem(DDP)of BNs.First,we prove that it would be better to adopt a special pinning strategy based on rank condition rather than randomly pinning and pinning strategy based on highest connection degree to achieve DDP solvability,based on which rank-conditions-based pinning state feedback controllers and output feedback controllers are designed,then the range of controllers' number is obtained.The results obtained is applied to the model of cell apoptosis.On the other hand,event-triggered control is proposed to solve the DDP.Triggered conditions are found and two kinds of effective algorithms are also proposed based on the redundant variable separation technique.Finally,we design the state feedback controllers and output feedback controllers to solve the DDP of dynamic-algebraic Boolean networks(DABNs),then sufficient conditions are also given to analyze the robustness of controllers concerning the DDP of the DABN with function perturbation.In addition,the results obtained is applied to the model of lac operon in the bacterium Escherichia coil.In chapter three,the robust output control invariant set of Boolean control net-works(BCNs)with disturbances is investigated.On the one hand,the necessary and sufficient condition is presented to analyze whether a given set is robust output con-trol invariant set or not under a given output feedback controller.On the other hand,output feedback controllers are designed under which a given set is a robust output control invariant set.In chapter four,we discuss function perturbations on the topological structure of DABNs.Then the local uniqueness of solution to the DABN is studied,under which the impacts of static function perturbations and dynamic function perturbations on the topological structure are investigated,respectively.In chapter five,we study the normalization of DABNs.A new algebraic expression of DABNs is proposed,based on which,the weaker normalization condition of DABNs is obtained.As its applications,the solvability and uniqueness of the solution to DABNs are investigated.Necessary and sufficient conditions on the solvability and the uniqueness are obtained.In chapter six,controllability of dynamic-algebraic BCNs is investigated based on a new normalization approach.Based on the obtained results in chapter six,some lower dimensional controllability matrices are defined such that the dimensions of matrices are much lower than that in other papers.Finally,some new necessary and sufficient conditions for the controllability are presented as well. |
PDF Full Text Request