布尔控制网络部分状态变量的稳定与镇定

Partial state stability and stabilization of Boolean control networks

系统的稳定与镇定是控制理论的重要研究内容.本文主要研究逻辑控制系统的部分状态变量的稳定与镇定问题,部分状态变量的稳定与镇定是一种特殊的稳定性概念,它只考虑状态变量中部分目标变量的稳定性与可镇定性.利用矩阵的半张量积,逻辑控制系统被表示为离散时间仿射线性系统.从系统的结构矩阵出发,首先给出逻辑系统的部分状态(一致)稳定的概念和部分状态(一致)稳定的条件,研究了逻辑控制系统部分状态变量的可镇定性,得到了部分变量通过常值控制序列或通过状态反馈控制器镇定的充要条件,并通过实例检验了所给条件的有效性.

The paper deals with problems on the stability and stabilization of Boolean networks with respect to a given part of variables characterizing the Boolean network. Using the semi-tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean （control） network can be converted to discrete time linear （bilinear） dynamics called the algebraic form of the Boolean （control） network. The two main results are as follows： （i） From the algebraic form of a Boolean （control） network, two partial stability definitions are intro- duced. One is partial stability with respect to another variable set, and the other is partial stability with respect to arbitrary initial states. （ii） Based on the algebraic form, necessary and sufficient conditions for the stability of global partial states with respect to the variable set and arbitrary initial states are obtained. Examples are provided to illustrate the effectiveness of our results.