In this paper, linear quadratic (LQ) optimal control problems are investigated for two types of uncertain random systems which consider the coefficient of the perturbed term as a constant vector or a vector-valued function of state vector and control vector. First, the uncertain random optimal control model is established under expected value criterion. Second, based on Bellman’s principle, recurrence equations are presented for settling such problem. Then by applying the recurrence equations and chance theory, the analytical expressions of the optimal results for the LQ problems are derived. Furthermore, some examples and an application are given to show the effectiveness of our results.

本文针对两种不确定的随机系统研究了线性二次（LQ）最优控制问题，该系统将被摄项的系数视为常数向量或状态向量和控制向量的向量值函数。首先，在期望值准则下建立了不确定的随机最优控制模型。其次，基于贝尔曼原理，提出了递推方程来解决该问题。然后运用递推方程和机会理论，推导了LQ问题最优结果的解析表达式。此外，给出了一些例子和一个应用来证明我们的结果的有效性。