Obsevability And Reconstructibility Of Switched Boolean Control Networks

In recent years,with the development of biological genetic research,many types of Boolean control networks have been derived.Among them,switched Boolean control networks play very important roles in theory and application.This paper involves three kinds of switched Boolean control networks.The main research contents are as follows:The first type:traditional switched Boolean control network,the observ-ability of it is mainly studied.Four types of observability are proposed for the first time.To describe the outputs driven by different input sequences and switching signals from each initial state,the observed data matrix is defined and four necessary and sufficient conditions are obtained to determine four types of observability,respectively.Moreover,the relationship among these four types of observability is discussed.The second type:switched Boolean control network with outputs con-taining synchronized switching signals,the reconstructibility of it is mainly investigated.Reconstructibility is the ability to determine the current state based on the known data.Four types of reconstructibility are proposed for the first time and two methods are provided.One is periodic method which com-pares the periodic state-model-input trajectories with the same period.The other is matrix method which constructs a matrix describing all initial states and their corresponding outputs driven by different model-input sequences.The third type:switched Boolean control network with outputs containing asynchronous switching signals,the reconstructibility of it is further explored.Seven definitions of reconstructibility are proposed where the existence and arbitrariness of the switching signal and the input sequence are inconsistent.A weighted pair graph describing all pairs of states which are indistinguish-able is defined.Combining this graph with automaton theory,a method for determining reconstructibility is given.Moreover,for a given reconstructible switched Boolean control network,an algorithm for determining the current state is provided.Finally,a state observer is designed.This paper is divided into five chapters:In Chapter 1,the research background of Boolean networks and Boolean control networks is briefly introduced.The research background of observa.bili-ty and reconstructibility and the existing research results are summarized.The related knowledge and applications of the semi-tensor product are introduced.Finally,the main research content and structure arrangement of this paper are outlined.In Chapter 2,the definition and properties of the semi-tensor product are introduced.Three types of switched Boolean control networks are presented.Under the framework of the structural matrix and the semi-tensor product,three algebraic forms of switched Boolean control networks are given.In Chapter 3,firstly,for the traditional switched Boolean control net-works,four definitions of observability are proposed.Based on the matrix method,some necessary and sufficient conditions for determining observabil-ity are given.Then,for the switched Boolean control network with outputs containing synchronized switching signals,four definitions of reconstructibili-ty are proposed.Based on the periodic method and the matrix method,the reconstructibility is studied respectively.In Chapter 4,for the switched Boolean control network with outputs con-taining asynchronous switching signals,seven types of reconstructibility are defined.Three algorithms are designed to construct different automata mod-els.Several necessary and sufficient conditions about reconstructibility are given.Finally,a state observer is designed.Chapter 5 summarizes the whole paper.