This paper addresses a version of the stochastic linear quadratic control problem on time scales , which includes the discrete time and continuous time as special cases. Riccati equations on time scales are given, and the optimal control can be expressed as a linear state feedback. Furthermore, we present the uniqueness and existence of the solution to the Riccati equation on time scales. Furthermore, we give an example to illustrate the theoretical results.

中文翻译：

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时间尺度上的随机线性二次控制问题

本文讨论了时标上的随机线性二次控制问题，其中包括离散时间和连续时间作为特殊情况。给出了时标上的Riccati方程，最优控制可以表示为线性状态反馈。此外，我们提出了时标上的Riccati方程解的唯一性和存在性。此外，我们举一个例子来说明理论结果。