Stability Analysis And Stabilization Design Of Switched Boolean Networks With Restricted Switching

Boolean network is an important mathematical model to study the evolution law of gene regulation network,and it also has important applications in ecosystems,intelligent robots,transportation,and other fields.In actual systems,the change of parameters,external environment or the asynchronization of internal node updating usually leads to the modal switching,and the switching signal generally has constraints,such as input constraints,state constraints,dwell time constraints and successor constraints,so it is of great significance to study the switched Boolean networks with restricted switching.In recent years,great progress has been made on the issues of stability,feedback stabilization,controllability,synchronization,and output tracking of Boolean networks with restricted switching.However,existing methods are mainly used to deal with static constraints.In this paper,based on the theory of semi-tensor product of matrices,we studied the stability and stabilization of Boolean networks with switching signals under dynamic constraints taking the example of successor constraints.Based on restricted switching signal dynamic generator and the semitensor product of matrices,the necessary and sufficient conditions for the set stability of the switched Boolean networks with restricted successors are obtained.Due to the memorability of switching signal with restricted successors,it cannot be processed by the existing static input transformation method.In order to solve this problem,a dynamic generator is constructed to make the output sequence set of the generator consistent with the constrained switching signal set.The method of constructing a switching generator is applied to the switched Boolean networks with restricted switching,and an unconstrained logical dynamic system is obtained.The stability of the system under arbitrary switching signals is equivalent to that of the original Boolean network with constraints.Based on this,the necessary and sufficient conditions for the set stability of the switched Boolean networks under restricted switching are derived.Finally,the results are used to analyze the dissipation problem of queued vehicles based on the logic model of intersection signal lights.The restricted switching signal dynamic generator method is applied to the stabilization problem of the switched Boolean control networks with restricted successors,and the criterion of stabilizability is obtained,and the design method of state feedback controller is given.The unconstrained switched logic dynamic network is obtained by connecting the switching generator and the Boolean control networks under restricted switching in series through the semi-tensor product of matrices.According to the properties of the switching generator,it is proved that the unconstrained switched logic dynamic system is equivalent to the original Boolean control network.On this basis,the necessary and sufficient conditions for the set stabilizability of the switched Boolean networks with restricted successors are derived.Finally,the design method of state feedback controller is given based on the theory of largest control invariant set.There are 21 figures,7 tables,and 78 references in this thesis.