The Study Of Stabilization Algorithm For Switched Boolean Networks

In the field of current biology,there is a close relationship between the gene regulatory networks and other biological systems such as neural networks and protein networks.Due to the fact that the Boolean networks(BNs)can well simulate the relationships among the genes,it is extensively utilized to model the biological systems in the past decades.Controllability and stabilization of BNs are important topics in control theory.In this paper,by using the semi-tensor product(STP)of matrices,the controllability/stabilization problems are investigated for the switching Boolean networks(SBNs),the relating switching signal sequences are also designed.The main work of this thesis is listed as follows.The first chapter introduces the background and summarizes the existed results of SBNs.Then,the definition and relating properties of STP of matrices are introduced,and the method for how to convert the dynamic equations of the BNs/SBNs to their equivalent algebraic forms by the theory of STP is also presented.At the same time,organization of the whole paper is stated.The second chapter studies the controllability problem of the SBNs.Some necessary and suffi-cient conditions are derived assuring the SBNs to be globally controllable by means of three different approaches,and the corresponding controllability algorithms are also given.The computational complexities for these three algorithms are compared,and it is concluded that each of them has its own advantages.Although the first method has the greatest computational complexity O(N~5),it contains the information of the switching signals.The second and the third one greatly reduce the computational complexity to O(N~4),but they cannot provide any information about the switching signals.The third one can be slightly adjusted so as to determine a special controllability for the SBNs.Finally,two examples are provided to illustrate the feasibility of the obtained criteria.The third chapter mainly addresses the stabilization problem and the design of the switching signal sequences for the SBNs.By constructing a series of Boolean matrices,a new matrix called the switching stabilization matrix is established based on which some necessary and sufficient condi-tions are presented guaranteeing the global stabilization of the SBNs.Then,based on the iteration idea,the method for establishing such a matrix and the corresponding algorithm are given,which can effectively reduce the computational complexity and therefore has certain practical significance.When the switching signals are state-dependent,by resorting to the state feedback gain matrix S,necessary and sufficient conditions are derived for the global stabilization of the SBNs.Unfortu-nately,the exact switching signal sequences still cannot be obtained from this matrix.Therefore,by transforming the global stabilization problem of the SBNs to an equivalent graphical description,the breadth-first in-tree search and the depth-first in-tree search are explored,which can not only get the exact switching signal sequence,but also reduce the time complexity in a certain degree.The forth chapter summarizes the contents of this paper.Moreover,some future works are also discussed.