Controllability Decomposition Of Dynamic-Algebraic Boolean Control Networks

In this paper,the controllability and controllability decomposition of dynamic-algebraic Boolean control networks are investigated.Considering the uncertainty of state transition of dynamic-algebraic Boolean control networks,two types of controllability of dynamic-algebraic Boolean control networks are firstly presented.Necessary and sufficient conditions of such controllability are derived.A similar concept of coordinate transformation called restricted coordinate transformation is posed.It is sufficient to transform the coordi-nate frame of a dynamic-algebraic Boolean control network and obtain its corresponding equivalent form.Relevant results about restricted coordinate transformation are proposed.Accordingly,two kinds of controllability decom-position axe discussed and the corresponding algorithms are provided,which differs from that of conventional Boolean networks.A method is provided to guarantee that all the dynamic equations in controllable subsystem are affect-ed by control.Furthermore,a numerical example and a practical example are given to demonstrate the results.In appendix,two further results are raised.On the one hand,the necessary and sufficient condition of observability of dynamic-algebraic Boolean control networks and the number of fixed points and cycles of it,is derived.On the other hand,a new approach to concept learning is given within the framework of semi-tensor product.The thesis consists of four chapters.In Chapter 1,the research background of controllability and controllability decomposition of dynamic-algebraic Boolean control networks is introduced.In Chapter 2,some expression forms of dynamic-algebraic Boolean control networks are shown.Besides,the definition of con-trollability and necessary and sufficient conditions of it,and special restricted coordinate transformation are presented.In Chapter 3,the definition of con-trollability decomposition,the necessary and sufficient condition of realizing it,and the algorithm are derived.Chapter 4 concludes the thesis.