论文标题
随机线性界面最佳控制，部分观察
Stochastic Linear-Quadratic Optimal Control with Partial Observation
论文作者
论文摘要
论文研究了一类针对部分可观察的线性动力学系统的二次最佳控制问题。与完整的信息案例相反，必须将控件适应观察系统产生的过滤，而观察系统又受控制的影响。在这种情况下，这种变化方法由于过滤不是固定的事实而失败。为了克服难度，我们使用状态过程的正交分解来写入成本功能为两个部分的总和：一个是控件的功能和滤波过程，另一部分是独立于控制的选择。第一部分具有类似于完整信息问题的数学结构。通过完成正方形，可以证明最佳控制是通过过滤过程通过反馈表示给出的。还明确获得了最佳值。
The paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the observation system, which in turn is influenced by the control. The variation method fails in this case due to the fact that the filtration is not fixed. To overcome the difficulty, we use the orthogonal decomposition of the state process to write the cost functional as the sum of two parts: one is a functional of the control and the filtering process and the other part is independent of the choice of the control. The first part possesses a mathematical structure similar to the full information problem. By completing the square, it is shown that the optimal control is given by a feedback representation via the filtering process. The optimal value is also obtained explicitly.
