Reconstructibility Analysis And Observer Design Of Probabilistic Boolean Networks

Boolean network,as an important model to simulate gene regulatory network,has attracted extensive attention since it was proposed.In recent years,due to the development of systems biology,many types of Boolean network have been derived.In addition to the Boolean control network(BCNs)with control input signal,switched Boolean networks and probabilistic Boolean networks(PBNs)play very important roles.This paper investigates the observability and reconstructible problem of Boolean control networks by using the semi-tensor product of matrix,and design state observer.The main contents of this paper are listed as follows:Firstly,the observability analysis of Probabilistic Boolean control networks(PBCNs).The distinguishability between different states is defined by means of state reachability set.Then,the observability of the system is analyzed by using state coupling method and finite automata method,and the conditions for determining the observability of the system are given.On this basis,for the probabilistic Boolean control network,the observability judgment matrix is constructed by using the state set,and an algorithm is designed to judge the observability of the system,and the initial state of the system is obtained at the same time.Then,the reconstructibility problem of probabilistic Boolean network is studied,and the state of the system is estimated.Three parts have been discussed with the reconstructibility problem of probabilistic Boolean network in this paper: the periodic reconfigurability of the system is discussed,four definitions of reconstructibility are given,and the discrimination methods are given for different definitions;the weighted pair graph of the system is obtained according to the finite automata,the vertex of the weighted pair graph is used to judge whether the system is reconstructibility,and the judgment theorem and algorithm of whether the system is reconstructibility are given;Finally,the reconstructibility in finite time is discussed,the reconstructible matrix of the system is given by means of state set,and an algorithm is designed to judge the reconstructibility of the system and current state of the system is obtained.Finally,the observer is designed according to the above-mentioned method to judge the reconstructibility of the system.Two design methods of state observer are given,which are the state observer based on finite time reconstructibility and the observer based on the principle of finite automata.Specific examples of the above discrimination methods are given by using MATLAB platform.At the end of this paper,the completed work is summarized,and the future research direction is further prospected.