Analysis And Control Of Boolean Networks With Unknown Function Structure

As a typical kind of networked control systems,Boolean networks(BNs)are an important mathematical model of gene regulatory networks.In practical gene regulatory networks,the network structure is easily known,but the node dynamics are often completely or partially unknown.Considering this fact,such a network is defined as a BN with unknown function structure.Using the algebraic state space representation method,this paper studies the stability,controllability and partial structural stabilization of BNs with unknown function structure.Firstly,the considered BNs and Boolean control networks(BCNs)with unknown function structure are converted to equivalent algebraic forms,respectively,which facilitates the use of classical control theory.Secondly,the concepts of point stability and set stability with probability one are given for the considered BNs with stochastic function structure.By defining the state transition probability matrix,necessary and sufficient conditions are proposed for judging whether the considered BNs with stochastic function structure is stable with probability one.Then,the concept of global stability with probability one is given for probabilistic Boolean networks(PBNs)with switching discrete probability distribution(DPD).By defining the state expectation matrix,a necessary and sufficient condition is presented for judging whether the considered PBNs with DPD is globally stable with probability one.Thirdly,the structural controllability matrix is defined by the equivalent algebraic form of BCNs,and sufficient and necessary conditions are given for the structural controllability of BCNs with unknown function structure.Finally,by defining the partial structural stabilization matrix,a criterion is given to verify the partial structural stabilization of BCNs with unknown function structure.