Feedback Controllability And Stabilization Problems Analysis Of Boolean Networks

As the Boolean model is a very good tool to model the relationships of genes in systems biology,more and more people are attracted to do research in this field,including biologists,physicists and systems control scientists,etc.While,the controllability of Boolean networks(BNs)is an very hot topic in this field.The research for controllability of BNs has received considerable attention.In this work,by using the semi-tensor product of matrices,we discuss the delayed feedback control for stabilization of Boolean Control Networks(BCNs)with state delay,the output tracking problem of BCNs,and the set stabilization of BNs under pinning control strategy.The main work of this dissertation are listed as follows:In Chapter 1,there is a brief introduction for the research state of BNs.Also some interesting works about the BNs are introduced in this chapter.In Chapter 2,some notions and knowledge about semi-tensor product of matrices are presented,including definition,lemmas,properties and so on.The way to construct the algebraic model of the BNs is also presented in this chapter.In Chapter 3,we study the delayed feedback stabilization problem for BCNs with state delay.Using the semi-tensor product of matrices,some necessary and sufficient conditions are obtained.For the stabilization of BCNs,detailed procedure to construct the feedback controllers is also presented.We further derive the number of different feedback controllers which can successfully stabilize the BCN in a finite time.An illustrative example is also presented to show the effectiveness of our method.In Chapter 4,we investigate the output tracking problem for the BCNs under a constant reference signal case.First,necessary and sufficient condition is presented to guarantee the successful output tracking of BCNs.Further,the maximum invariant set is obtained to realize the output tracking in the shortest time,and based on the invariant set,the number of different state feedback matrices which make the output tracking successful is explicitly expressed.Computational cost can be largely reduced by using our method.Finally,an illustrative example concerning the lac operon in the bacterium Escherichia Coli is given to illustrate the proposed method.In Chapter 5,we study the set stabilization of BNs under pinning control strategy.First,the algebraic expression of BN is obtained by using semi-tensor product of matrices.Based on the algebraic expression,we give a method to choose pinning nodes.We achieve set stabilization by controlling the pinning nodes.A matrix is defined in advanced to construct the state feedback controller.Based on the matrix set,state feedback controller can be obtained quickly and the computational complexity can be reduced.Finally,an example is given to illustrate the design procedure of pinning controllers.In Chapter 6,a brief conclusion is presented to end this work,also the prospect for the work is made.