In this paper, we study the approximate optimal control problems for a class of fractional partial stochastic differential inclusions driven by Rosenblatt process and non-instantaneous impulses in a Hilbert space. Firstly, we prove an existence result of mild solutions for the control systems by using stochastic analysis, the fractional calculus, the measure of noncompactness, properties of sectorial operators and fixed point theorems. Secondly, we derive the existence conditions of approximate solutions to optimal control problems governed by fractional impulsive partial stochastic differential control systems with the help of minimizing sequence method. Finally, an example is given for the illustration of the obtained theoretical results.

在本文中，我们研究了由Rosenblatt 过程和Hilbert 空间中的非瞬时脉冲驱动的一类分数部分随机微分包含的近似最优控制问题。首先，利用随机分析、分数阶微积分、非紧性测度、扇形算子的性质和不动点定理证明了控制系统温和解的存在性。其次，借助最小化序列方法，推导了分数阶脉冲偏随机微分控制系统最优控制问题近似解的存在条件。最后给出一个算例来说明所得的理论结果。