Research On Optimal Control Problem For A Class Of Logical Network Systems

Boolean network is a powerful tool to describe the interaction between genes in system biology,such as gene regulation and cell differentiation.In recent years,with the rapid development of system biology,the research of Boolean network system has become one of the hot issues of scholars.This thesis mainly studies the optimal control problem of Boolean network dynamic system.Firstly,we apply the semi-tensor product between matrices to transform the optimal control problem of Boolean dynamic network system into the optimal control problem of equivalent discrete control system,and then use the idea of dynamic programming method to solve the problem.Secondly,Studying the solution of the optimal control problem in finite horizon.By introducing a new variable to transform this constrained optimization problem into an unconstrained optimization problem,we give a new algorithm for solving the problem.Furthermore,the solvability of the optimal control problem is proved in the infinite horizon.Based on the approximation theorem,the method for finding the approximate solution of the optimal control problem for Boolean dynamic networks is given in an infinite horizon.Finally,the new solutions to the optimal control problem in the finite horizon and the infinite horizon are used to solve the specific examples.The thesis makes full use of post-conversion problem by the semi-tensor product between matrices.The system and target functional are both the advantages of state and control bilinear expression and the Boolean network logic variables can only take the characteristics of 0 and 1.For solving the problemin in the finite horizon,compared with the classical dynamic programming method,the algorithm can save storage space and computational quantity,and implement computer programming easily.It has certain innovations.The conclusion of this thesis enriches the dynamic control system of Boolean network and the optimal control theory.The research content can also provide a kind of calculation method for the practical application of Boolean network system optimal control.