Observability,identification And Synchronization Control Of Boolean Networks With Time Delay

With the rapid development of systems biology,its research techniques have gradually transitioned from phenotypic analysis to modeling,analysis and control of complex biological systems.As the regulatory networks simulating gene interactions,Boolean networks,have become the research focuses and hot spots in bioinformatics field.However,due to environmental factors in the practical applications,such as gene mutations and drug reactions,etc,the state update or trajectories of Boolean networks may exist some inevitable delayed reactions.As the generalization of traditional Boolean networks,Boolean networks with time delay can effectively model various kinds of delay phenomena in biological systems,but their analysis and control problems are becoming more complicated.Using the semi-tensor product(STP)theory,we study observability,identification and synchronization control of Boolean networks with time delay to further improve the theoretical framework of logical dynamic networks.The main contents of this thesis are as follows:Chapter 1 introduces the background and significance of this thesis,which include:the background of Boolean networks with time delay,the applications and development of the semi-tensor product theory,and the current research status of delayed Boolean networks in observability and detectability,identification and synchronization.Chapter 2 firstly outlines the basic theory of matrix semi-tensor product including the definition and basic properties.Secondly,the algebraic forms of(delayed)Boolean(control)networks are given under the framework of the semitensor product.Chapter 3 investigates the observability and detectability of Boolean control networks with time delay and injection mode.By dividing the states,inputs and outputs,the original network with time delay is equivalently segmented into several sub-networks without time delay.Using the state transition matrix and output matrix of the sub-networks,the output and state parameter matrices are constructed under the free and networked inputs.Then by the constructed parameter matrices,two types of equivalent relation are established to reflect the state information with the same input-output data.Subsequently,the necessary and sufficient conditions for several kinds of observability and detectability of Boolean control networks with time delay are given via observability and detectability matrices.Chapter 4 gives the definitions of identification about delay parameter and network structure of Boolean(control)networks with time delay.By using the state and input-output partitioning method,the original network is regarded as the combination of several sub-networks with the same structure and no time delay.According to the relationship between the original network and the subnetworks on output sequences,the calculative methods of delay parameters are given.Then,based on the obtained input-output data,the necessary and sufficient conditions for identification of network structure are presented.Meanwhile,the specific methods are proposed to reconstruct the network structure.In Chapter 5,focusing on the synchronization of group behavior in the practical context,the delay synchronization of drive-response Boolean(control)networks is studied.According to whether delay steps depend on the initial states,two definitions of delay synchronization are proposed to achieve the theoretical extension of synchronization.For the driven-response Boolean network with time delay,two conditions for delay synchronization are given by using the limited set theory.For the driven-response Boolean control network with time delay,the criteria for two kinds of delay synchronization are obtained via the set stabilizable methods.And the effective algorithms of state feedback controllers are established to achieve two kinds of delay synchronization with the shortest steps,respectively.In Chapter 6,we give the summary of this thesis and the future research work prospects.