Analysis And Control Of Switched And Delayed Boolean Networks Via The Semi-tensor Product Method

The Boolean network is an effective model to describe gene regulatory networks,whose theoretical research is of great value to explore the mechanism of life activities,the cause and treatment of diseases.At present,it becomes a research hotspot in control domain.Using the semi-tensor product of matrices,the dynamic equations of Boolean networks can be transformed into an equivalent algebraic form,which provides a unified theoretical framework to research Boolean networks.In this dissertation,the observability,controllability and set controllability of periodically switched Boolean control networks(PSBCNs)are discussed,and the robust stability and stabilization problems of delayed Boolean networks with disturbances are studied.The main contents are listed as follows:1.Observability of PSBCNs is studied.First,the algebraic state space representation of a PSBCN is given.Then,a parallel system is constructed and the observability problem of the original PSBCN is transformed into the set reachability problem of the parallel system.Based on which,two necessary and sufficient conditions are obtained to detect reachability of the parallel system and observability of the PSBCN.In addition,the proposed results are extended to the case of state constraints.Finally,the Boolean model of lactose operon in Escherichia coli is used to verify the conclusions.2.Controllability and set controllability of PSBCNs are studied.First,the algebraic form of switching signal is given and a parallel system is formed by combining the switching signal and the state.Then the controllability problem of PSBCNs is transformed into the set controllability problem of the new system,and the criterion for controllability is obtained.Second,the set controllability matrix of PSBCNs is constructed,and the necessary and sufficient condition of set controllability for the system is presented.Moreover,a more general PSBCN is considered and the criteria for its controllability and set controllability are proposed.Finally,the results are applied to the apoptosis networks.3.Robust stability and stabilisation of delayed Boolean networks are studied.First,the algebraic form of a delayed Boolean network with disturbance is given.Based on the theory of robust trajectory stability,robust stability of the system is studied and the corresponding criterion is derived.Second,the robust stabilisation and controller design problems are considered.Based on the algebraic representation of a delayed Boolean control network and the theory of robust trajectory stabilisation,a necessary and sufficient condition is established to detect robust stabilisation of the system,moreover,the corresponding state feedback controller is designed.Finally,an illustrative example is displayed to support our new results.