Research On Output Tracking And Set Stabilization Of Boolean Network

Boolean networks(BNs)are an important model of system biology,they have a simple structure and abstract description features,which have attracted wide attention from genetic scientists.In recent years,Cheng et al.have proposed the semi-tensor product(STP)theory of matrices.Using this theory,we can transform the logical form of BNs into algebraic form,which facilitates the research of BNs.BN model has been applied to many fields,such as biology,game theory,information science and so on.While,the controllability of BNs is a hot issue in this field.In this paper,we mainly discuss robust output tracking of delayed BNs under pinning control and set stability for switched BNs with open-loop and closed-loop switching signals.The main content of this paper is arranged as follows:In the first chapter,we first introduce the research background and research status of Boolean network.And then,to derive the desired result successfully,some fundamental definitions and lemmas are introduced in the preliminary knowledge part.In the second chapter,a class of robust output tracking problems for delayed Boolean control networks(BCNs)is considered under pinning control.First,we give the algebraic representation for such networks,and a criterion is derived on one step robust reachability.And then,a constructive program is presented to design feedback pinning controllers.With the use of these controllers,output tracking is achievable.Further,an algorithm and a procedure are given to find the time-optimal pinning controllers.Finally,an example is shown to illustrate the advantages and better innovation of the proposed approach.In the third chapter,we investigate the set stability of switched BNs by consid-ering two different methods of switching signals in the form of open-loop and closed-loop switching.First,the definitions of set stability are proposed for switched BNs with such switching signals.Then,we propose two different algorithms to find the largest open-loop switching invariant set and largest closed-loop switching invariant set.Furthermore,the corresponding set stability conditions for switched BNs are given in each case.In addition,the constructive procedures are presented to design the switching signal sequence to achieve set stability under the two different meth-ods of switching signals.Finally,the effectiveness of the proposed algorithms and research results are demonstrated using two numerical examples.Finally,the fourth chapter summarizes the research work of this dissertation and provides some trends of future research.