Optimal control problems governed by two different types of uncertain discrete-time singular systems are investigated under expected value criterion. The objective function including uncertain variables is optimized with the help of expected value method provided that the singular systems are both regular and impulse-free. At first, based on the principle of dynamic programming, a recurrence equation is derived to simplify an optimal control model for a class of uncertain discrete-time singular systems. After that, according to uncertainty theory and the recurrence equation, two kinds of optimal control problems subject to an uncertain linear singular system and an uncertain singular system with quadratic input variables are considered in order, and the optimal solutions are both presented by accurate expressions. A numerical example and a dynamic input-output model are settled to illustrate the effectiveness of the results obtained.

在期望值准则下研究了由两种不同类型的不确定离散时间奇异系统控制的最优控制问题。如果奇异系统既是规则的又是无脉冲的，则借助于期望值方法可以优化包括不确定变量在内的目标函数。首先，基于动态规划原理，推导了一个递推方程，简化了一类不确定离散时间奇异系统的最优控制模型。然后，根据不确定性理论和递推方程，依次考虑了不确定线性奇异系统和具有二次输入变量的不确定奇异系统的两种最优控制问题，并通过精确表达式给出了最优解。