Analysis And Control Of Logical Dynamic Systems With Time Delay Yating Zheng

With the rapid development of medical science and systems biology,delayed logic system has been widely studied as an important model of gene regulatory networks in the past half century.Using the algebraic state space representation method,this paper studies the attractor,stability,stabilization,tracking control and disturbance decoupling of delayed logic systems.Firstly,the matrix semi-tensor product method is used to convert the delayed logic system into a linear form,and the state-based delayed logic system is converted into a trajectory-based logic system through the state expansion.Both forms are proved to be equiva-lent with respect to the issues studied,which facilitates the use of classical con-trol theory to study delayed logic systems.Secondly,the concepts of controllabil-ity?reachability?stability?stabilization?tracking and decoupling of logic system are redefined in the logic system based on trajectory.The methods for finding the attractors and calculating the number of attractors of logic systems are given.A necessary and sufficient condition for the stability of delayed logic network is ob-tained by studying the trajectory transition matrix.Using the idea of splitting matrix,a new matrix based on the trajectory transition matrix is constructed to study the necessary and sufficient conditions for stabilization?set stabilization and tracking of the delayed logic control system.A controller that makes the delayed logic system reach the target state is designed.The disturbance decoupling prob-lem of delayed logic control system is studied through coordinate transformation,and a controller design method that decouples the network is given.Moreover,the above problems are further generalized to constrained systems.The problems such as attractor?stability?stabilization?tracking control?and disturbance decoupling of delayed logic systems with state constraints or input constraints are discussed.Some sufficient and necessary conditions are obtained.Finally,the results obtained are applied to delayed logic system modeled by the biological network,such as the coupled oscillations in the cell cycle and lac operon in the bacterium Escherichiacoli to show the effectiveness of the obtained results.