Online Observability Of Boolean Control Networks

Boolean Control Network(BCN)is a model that is often used when modeling biological systems.To make better use of this model in studying biological systems,researchers need to conduct more in-depth research on its control theory.The control theory of BCN is based on its various control-theoretical properties.These properties mainly include controllability,observability,detectability and identifiability.The main content of this master thesis is about the observability of BCNs.The topology of a BCN is a directed graph.This directed graph contains three types of nodes: input-nodes,state-nodes,and output-nodes.Each node can be regarded as a Boolean variable,and the values of these nodes evolve at discrete time points.The edges of a directed graph represent the interaction between nodes.The specific form of the interaction between nodes is characterized by the updating rules of the BCN.For a BCN,we can only directly control the values of its input nodes and the values of its observation output nodes,and we cannot directly control or observe its state nodes.The observability of a BCN is proposed to study if is possible and how to determine the value of the state node at the initial moment(also called the initial state)through the values the input nodes and output nodes of the BCN when we know the updating rules of it.Because in different application scenarios,researchers need to use different algorithms to determine the initial state,the researchers proposed different types of observability to characterize whether the initial state of the BCN can be determined by these algorithms.There are four types of observability have been proposed,but our analysis finds that none of the four types of observability characterizes the property that the initial state of the BCN can be determined when the initial state cannot be reset i.e.single experiment observability.Therefore,in this thesis we propose a new type of observability named online observability to characterize this property.The main contributions of this thesis are as follows.1.We proposed an online observability and an algorithm to determine the initial state.This will enable researchers to determine the initial states of more BCNs when the initial states cannot be reset.And this also correct a claim that one of the existing four types of observability as the single experiment observability.2.We prove that the online observability which we define above together with controllability is the necessary and sufficient condition of the identifiability of BCN.We believe this an essential characterization of the identification problem of BCN,and show the relation between the contro-theoretical properties of BCNs.3.We propose a new online detectability based on our online observability and the relationship between observability and detectability,and we give two algorithms to decide if a BCN is online observable and online detectable,respectively.In summary,the work presented in this dissertation improves the current state of the control theory of BCNs,including formal definitions of online observability and online detectability,their decision algorithms,and theories about relationship between identifiability and online observability.