| In this paper,we mainly study the detectability of mix-valued logical net-works.With the help of semi-tensor product theory of matrix,the logical dynamic equations of logical networks can be transformed into discrete algebraic equations.On this basis,we establish the data form of mix-valued logical networks.Accord-ing to the data form of mixed valued logic network,its detectability is analyzed systematically.In addition,the detectability of probabilistic mix-valued logical networks is studied.The specific contents include:The first chapter introduces the related research of mix-valued logical net-works,the general situation and application of semi tensor product,and the research status of detectability.In the second chapter,we introduce the theory of semi-tensor product of matrix and some basic properties,and how to get the equivalent algebraic form of logical networks by means of semi-tensor product.In the third chapter,the concepts of different types of detectability of mix-valued logical control networks and mix-valued logical networks are given firstly,then the data form of mix-valued logical control network is established,the con-struction method is given,the necessary and sufficient conditions of detectability of mix-valued logical control networks and mix-valued logical networks are given,and the related algorithms are designed.Finally,the relationship between de-tectability and stabilizability of mix-valued logical control networks is analyzed.In the fourth chapter,we first introduce the probabilistic mix-valued logical networks,and give the definitions of strong and weak detectability.Secondly,the concept and establishment method of data form and detection form are given.Then,based on the detection form,the necessary and sufficient conditions for strong and weak detectability of probabilistic mix-valued logical networks are given,and the corresponding algorithms are designed.Finally,the relationship between detectability and stability of probabilistic mix-valued logical networks is analyzed.The fifth chapter summarizes the main conclusions and puts forward the future research direction. |
