This paper primarily focuses on LQ optimal control problem of fractional-order discrete-time systems based on uncertainty theory that is a significant tool to model belief degree. First, an equivalent LQ problem, which is integer-order one, is presented by expanding the state variables with the unchanging control variables. This equivalent problem is then solved by dynamic programming approach. Accordingly, the solution of the proposed LQ optimal control problem reduces to solve a system of backward matrix difference equations. Finally, a numerical example is provided to show how to solve the proposed LQ optimal control problem. As an application, an LQ optimal control problem of macroeconomic system is discussed by the achieved results.

本文主要基于不确定性理论研究分数阶离散时间系统的LQ最优控制问题，不确定性是建模置信度的重要工具。首先，通过用不变的控制变量扩展状态变量，提出了一个等效的LQ问题，它是整数阶。然后，通过动态编程方法解决该等效问题。因此，所提出的LQ最优控制问题的解决方案减少以求解后向矩阵差分方程组。最后，通过数值例子说明了如何解决所提出的LQ最优控制问题。作为一个应用，通过所取得的成果讨论了宏观经济系统的LQ最优控制问题。