Stabilization Of Switched Boolean Networks Via Semi-Tensor Product

This dissertation investigates the stabilization problem of switched Boolean networks.By using the semi-tensor product of matrices,switched Boolean net-works can be transformed into their equivalent algebraic form.On this basis,the stabilization and set stabilization of switched Boolean networks are researched,respectively.Specifically:Chapter 1 introduces the research background of this dissertation,includ-ing:definition and properties of semi-tensor product and its application in sys-tem theory and engineering practice,the origination and development of switched Boolean networks,and the research status of stabilization of switched Boolean networks.Chapter 2 introduces the basic knowledge needed in this dissertation,in-cluding:how to use the semi-tensor product to obtain the algebraic forms of switched Boolean networks,the problem description of stabilization and set sta-bilization of switched Boolean networks.In Chapter 3,with the help of the algebraic forms of switched Boolean networks and Warshall algorithm,an explicit criterion for the stabilization of switched Boolean networks is presented.Moreover,by analyzing the state transi-tion matrix of switched Boolean networks,an improved algorithm for calculating the largest control invariant set is proposed.In addition,an explicit criterion is derived to check whether a switched Boolean network satisfies set stabiliza-tion.Compared with the existing results,our results are easier to implement by computer.In Chapter 4,set controllability is introduced into the study of stabilization of switched Boolean networks.Firstly,the definition of set controllability of switched Boolean networks is given.Secondly,the set controllability matrix can be obtained by iterating the state transition matrix of switched Boolean networks.On this basis,the necessary and sufficient condition for the solvability of set stabilization is obtained.Furthermore,the proposed method for designing the switching signals drives the switched Boolean networks to be set controllability.In Chapter 5,we introduce the flipping mechanism for switched Boolean networks whose stabilization problem or set stabilization problem is unsolvable.That is to say,for any switching signal sequence,we can not find a control input sequence such that all states can reach and remain in a given target state or state set.For above-mentioned switched Boolean networks,we will discuss whether the stabilization or set stabilization can be transformed from unsolvable to solvable by means of flipping mechanism.The main results of this chapter include:the necessary and sufficient conditions for the solvability of stabilization and set sta-bilization of switched Boolean networks by flipping mechanism,are established;Two algorithms for calculating the minimum number of flipped nodes needed to make the stabilization and set stabilization of switched Boolean networks solvable are given.In the aspect of controller design,in order to reduce the control cost as much as possible,event-triggered control strategy is introduced in Chapter 6 for the stabilization of switched Boolean networks.Firstly,the event-triggered conditions for stabilization and set stabilization are proposed,respectively.On this basis,the methods are presented to obtain all possible event-triggered state feedback controllers for stabilization and set stabilization of switched Boolean networks.Chapter 7 of this dissertation investigates the finite-time stabilization prob-lem of Markovian jump Boolean networks.Firstly,on the basis of converting Markovian jump Boolean networks into Markov chains,a necessary and sufficient condition for the finite-time stabilization of Markovian jump Boolean networks is put forward.Secondly,pinning control is introduced to the finite-time stabi-lization of switched Boolean networks.Furthermore,an algorithm for calculating minimum number of pinning nodes is devised by altering the transition proba-bility matrix of Markov chains.Finally,a method for designing all the required pinning state feedback controllers is proposed.In Chapter 8,we give the summary of this dissertation and the future research work prospects.