Research On Control Problems Of Boolean Control Networks With Time-delay

With the development of human genome sequencing technology,the research of gene regulation networks has become a hot topic in systems biology.A Boolean network is a special discrete dynamic system expressed by binary logic variables and logic functions.It can well simulate the nonlinear dynamic behavior in the process of gene network control,and further reveal the evolution law of gene control network.So Boolean networks are a powerful tool for describing,analyzing,and simulating genetic regulation networks.The dynamic process of Boolean networks contains a large number of logical operations.Due to the lack of necessary mathematical tools for logical expressions,the theoretical study of Boolean networks is relatively weak.In recent years,with the development of the semi-tensor product of matrices,the logic operation can be transformed into matrix operation under the definition of structure matrices,and the transformation of Boolean control networks can represent the logic dynamic system as an algebraic state space dynamic system.The classical control problem of Boolean network is studied by using the semi-tensor product of matrix,and the complete theoretical framework of Boolean control network is formed.Observability problem is one of the fundamental problems of control systems.Because the phenomenon of delay exists widely in nature,it is of great significance to study the observability of time-delay Boolean networks.Because of the nonlinearity of Boolean control networks,there are four different types of observability.In this paper,we mainly study the verification methods of many kinds of observability definitions in the case of time delay.For Boolean control networks,people always want to control the state of the system to achieve the desired output.In order to achieve this goal,the method of designing feedback controllers is usually adopted.The design of the controller is extended to design the controller based on state feedback when the time delay is constant.