时滞对逻辑网络优化控制的影响

The Effect of Time Delay on the Optimization Control of Logical Networks

分析了包含两种个体的逻辑网络的时滞优化控制。其中第1种被称为机器的个体策略是固定的;第2种被称为人的个体具有自适应性,即能根据系统的整体状态做出策略的调整。以矩阵的半张量积作为逻辑分析的工具,分析了在状态时滞和输入时滞的影响下使人的收益最大的最优控制问题。理论分析显示状态时滞导致最优控制策略的周期长度增加,但人的最大收益值不会改变。最后提出仿真算法,其数值结果与理论结果一致。

This paper investigates the optimal control with time delay of the. logical network that consists of two kinds of agents called machine and human, respectively. The former has a fixed strategy whereas the latter can adaptively modify its strategy according to the state of the system. By means of the semi-tensor product of matrix technique, we solve the optimization problem of maximizing the payoff of huma~： in the presence of time delay in states and inputs. The theoretical analysis indicates that the period of the optimal control strategy becomes longer due to the delay in states, but the maximum payoff does not change. We also propose a simulation algorithm. The numerical results thus obtained are in good agreement with the theoretical results.