Analysis And Control Of Boolean Networks

Boolean networks(BNs)as models of Gene regulatory networks have attracted considerable research attention since they were first proposed by Kauffman in 1969.With the rapid development of systems biology,BNs have become a hot research topic in the current control field.By resorting to the semi-tensor product(STP)technique,BNs can be equivalently converted into an algebraic form which heavily facilitates the analysis of BNs,thereby promotes the development of BNs.This dissertation surveys the author's main works on dynamic analysis,control theory and state estimation of BNs during the period of pursuing his doctorate.The controllability problem of Boolean control networks(BCNs)is studied.By resorting to the STP technique and the Warshall algorithm,several improved novel reachability and controllability criteria are obtained for the BCNs.By constructing a sequence of Boolean matrices,controllability matrix of the considered BCNs is derived iteratively.It is worth pointing out that the proposed method has lower computational complexity,and thus facilitates the reachability and controllability analysis for BCNs.In addition,the issue concerning controllability of BCNs with undesirable interior states is investigated.Autonomous Boolean networks,which are developed to model the BNs with regulatory delays,are well known for their advantages of characterizing the intrinsic evolution rules of biological systems,such as the gene regulatory networks.Motivated by such a background,this dissertation aims to investigate the controllability of Autonomous Boolean control networks with pinning controllers.Several necessary and sufficient criteria are provided based on the STP of matrices.Moreover,a pinning control algorithm is presented for steering an Autonomous Boolean network from any given states to the desired state in the shortest time period.Some algorithms for state feedback stabilization of BCNs are developed.By resorting to the STP technique,the labelled digraph that can be used to completely characterize the dynamics of BCNs is derived,which leads to an equivalent graphical description for the stabilization of BCNs.What is more interesting is the fact that the existence of a state feedback controller stabilizing the BCN to a certain equilibrium point can be characterized in terms of its spanning in-tree.Consequently,two in-tree search algorithms,namely,the breadth-first search and the depth-first search,are proposed to design the state feedback stabilizing law when the global stabilization is feasible.Besides,some basic properties of the tree-search algorithms are addressed.This dissertation addresses the output regulation problem of BCNs in the presence of exogenous disturbances.By using the STP technique,the BCNs with stochastic perturbations are represented in their compact algebraic forms,and then a relating augmented system is constructed,which facilitates the analysis of the output regulation problem for the BCNs.As a consequence,necessary and sufficiency criteria are obtained to ensure the existence of the state feedback controllers.Moreover,an executable constructive procedure is also proposed for the controller design.Several necessary and sufficient criteria are established for the general synchronization of different families of BNs.The complete synchronization problem is investigated for the drive-response switched Boolean networks(SBNs)under arbitrary switching signals,where the switching signals of the response SBN follow those signals generated by the drive SBN at each time instant.Firstly,the definition of complete synchronization is introduced for the driveresponse SBNs under arbitrary switching signals.Secondly,the concept of switching reachable set starting from a given initial states set is put forward,from which a necessary and sufficient condition is derived for the complete synchronization of the drive-response SBNs.In addition,a simple algebraic expression for the switching reachable set in a given number of time steps is obtained,and two computable algebraic criteria are presented for the complete synchronization of the SBNs.The reachable-set-based approach is convenient and efficient when expressing and analyzing the limit set of BNs.Based on it,this dissertation studies the synchronization of different families of BNs including interconnected Boolean networks,probabilistic Boolean network,BNs with stochastic disturbances.A general theoretical framework is developed for the state estimation problem of stochastic time-varying Boolean networks(STVBNs).The STVBN consists of a system model describing the evolution of the Boolean state and a model relating the noisy measurements to the Boolean state.Both the process noise and the measurement noise are characterized by sequences of mutually independent Bernoulli distributed stochastic variables taking values of 1 or 0.First,an algebraic representation of the STVBNs is derived based on the STP.Then,according to the Bayes' theorem,a recursive matrix-based algorithm is obtained to calculate the one-step prediction and estimation of the forward/backward state probability distribution vectors.Owing to the Boolean nature of the state variables,the Boolean Bayesian filter is designed that can be utilized to provide the minimum mean-square error state estimate for the STVBNs.In addition,the fixed-interval smoothing filter is also obtained by resorting to the forward-backward technique.Finally,a state-vector-augmentation method is presented to deal with colored process/measurement noises.