Chance theory provides us a useful tool to solve an optimal control problem with indeterminacy composing of both uncertainty and randomness. Based on chance theory, this paper studies an optimal control for uncertain random singular systems with multiple time-delays. First, an uncertain random singular system with multiple time-delays is introduced, and then the corresponding optimal control problem is established. The equivalent relationship between this problem and the optimal control problem for standard uncertain random systems is derived. Then the appropriate recurrence equations are proposed according to the dynamic programming method. Furthermore, two kinds of optimal control problems are discussed. The optimal control inputs and respective optimal values of the problems are provided via the solvability of the obtained equations. Finally, a numerical example is presented to show the effectiveness of our theoretical results.

机会理论为我们提供了一个有用的工具来解决由不确定性和随机性组成的不确定性的最优控制问题。本文基于机会理论，研究了具有多重时滞的不确定随机奇异系统的最优控制。首先介绍了一个具有多重时滞的不确定随机奇异系统，然后建立了相应的最优控制问题。推导出该问题与标准不确定随机系统最优控制问题的等价关系。然后根据动态规划方法提出合适的递推方程。此外，还讨论了两种最优控制问题。问题的最优控制输入和各自的最优值通过所获得方程的可解性提供。最后，