一类无穷时域上布尔网络最优控制问题的求解方法

A Method for Solving a Class of Optimal Control Problem of Boolean Networks on Infinite Horizon

摘要: 布尔网络是描述基因调控、细胞分化等系统生物学的有力工具。布尔网络系统的最优控制问题已经成为当前控制领域的研究热点问题之一。本文主要研究布尔网络系统取目标泛函最大化的最优控制问题。首先，给出有限时域上问题的求解方法；其次，在该方法的基础上，对无穷时域上的问题进行研究，给出无穷时域上目标泛函最大化的布尔网络最优控制问题的可解性和求解方法；最后，将方法应用到一个具体的实例上。

Abstract: Boolean network is a powerful tool for describing biological system, such as gene regulation and cell differentiation. The optimal control problem of Boolean networks system has become one of the hot research issues in the field of control on the current. In this paper, we mainly study the optimal control problem of the Boolean network system to maximize the target functional. Firstly, we give the solution method of the problem in finite horizon; secondly, based on the method, the problem in infinite horizon is studied, as well as we give the solvability and solution method of the problem in infinite horizon; in the end, we apply our method to a concrete example.