具有随机场系数的随机最优控制问题计算已成为研究的新热点，但当前主要成果局限于控制受限的随机最优控制问题，缺少对状态受限随机最优控制问题计算方法的研究。本研究拟采用局部加密的自适应随机Galerkin有限元方法研究具有随机场系数的两类状态受限积分微分方程最优控制的数值逼近和理论分析,发展其高效数值方法。具体如下：1）研究两类状态受限随机积分微分方程最优控制的随机Galerkin有限元积微分全离散方法，研究分析其计算格式的收敛性等以获得最优阶的先验误差估计2）采取基于紧支集径向基函数的无网格方法和经典有限元方法逼近状态受限随机最优控制，推导随机空间和物理空间上的联合后验误差估计3）对以上随机积分微分方程最优控制问题发展出随机空间局部加密的自适应计算方法，进行各种规模的数值模拟实验。以上这些研究创新都属于当今前沿领域，非常具有挑战性，可以相信这些创新将对随机最优控制整体创新起到重大的推动作用。

In recent years, efficient numerical methods for optimal control problems governed by partial differential equations with random field coefficients are becoming a new hot topic. However, the works for computation of random optimal control currently focus on control constrained random optimal control , and there is still a lack of research on computational methods for state constrained random optimal control. In this work, we aim to study state constrained optimal control problems governed by two kinds of integral-differential equations with random field coefficients by using Stochastic Galerkin finite element methods and adaptive local refinement methods. In particular, the following aspects are discussed. 1) We study the state constrained optimal control problems governed by two kinds of random integral-differential equations, and analyze the convergence of the computational schemes to obtain the optimal error estimates 2) We approximate state constrained random optimal control problems by using meshfree method based on compactly supported radial basis functions and classic finite element methods, and derive the a joint posterior error estimate on random space and physical space 3) We develop adaptive local refinement methods on random space for the state constrained optimal control problems governed by two kinds of integral-differential equations, and conduct various numerical experiments. The above research innovations are on today's frontier and are very challenging. We believe these research innovations will play a significant role in promoting the overall progress on computation of optimal control.