论文标题
内存限制的部分可观察到的随机控制及其平均场控制方法
Memory-Limited Partially Observable Stochastic Control and its Mean-Field Control Approach
论文作者
论文摘要
在许多实际情况下，具有不完整信息和记忆限制的控制问题出现。尽管部分可观察到的随机控制（POSC）是一个常规的理论框架，它考虑了最佳的控制问题，但它无法考虑记忆限制。此外，除特殊情况外，在实践中不能解决POSC。为了解决这些问题，我们提出了一个替代的理论框架，即记忆限制的POSC（ML-POSC）。 ML-POSC直接考虑记忆限制和不完整的信息，并且可以通过采用均值场控制理论的数学技术来解决它。 ML-POSC可以将LQG问题推广到包括内存限制。由于估计和控制在LQG问题和内存限制的LQG问题中没有明确分开，因此将Riccati方程式修改为可观察到的Riccati方程，从而改善了估计和控制。此外，我们通过将ML-POSC与局部LQG近似进行比较来证明ML-POSC对非LQG问题的有效性。
Control problems with incomplete information and memory limitation appear in many practical situations. Although partially observable stochastic control (POSC) is a conventional theoretical framework that considers the optimal control problem with incomplete information, it cannot consider memory limitation. Furthermore, POSC cannot be solved in practice except in the special cases. In order to address these issues, we propose an alternative theoretical framework, memory-limited POSC (ML-POSC). ML-POSC directly considers memory limitation as well as incomplete information, and it can be solved in practice by employing the mathematical technique of the mean-field control theory. ML-POSC can generalize the LQG problem to include memory limitation. Because estimation and control are not clearly separated in the LQG problem with memory limitation, the Riccati equation is modified to the partially observable Riccati equation, which improves estimation as well as control. Furthermore, we demonstrate the effectiveness of ML-POSC to a non-LQG problem by comparing it with the local LQG approximation.
