Tottori Takehiro, Kobayashi Tetsuya J
Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8654, Japan.
Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.
Entropy (Basel). 2022 Nov 3;24(11):1599. doi: 10.3390/e24111599.
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 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 technique of mean-field control theory. ML-POSC can generalize the linear-quadratic-Gaussian (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 for a non-LQG problem by comparing it with the local LQG approximation.
信息不完全和记忆限制下的控制问题出现在许多实际情况中。尽管部分可观测随机控制（POSC）是一个考虑信息不完全时最优控制问题的传统理论框架，但它无法考虑记忆限制。此外，除了特殊情况外，POSC在实际中无法求解。为了解决这些问题，我们提出了一个替代的理论框架，即记忆受限POSC（ML-POSC）。ML-POSC直接考虑记忆限制以及信息不完全，并且可以通过运用平均场控制理论技术在实际中求解。ML-POSC可以将线性二次高斯（LQG）问题进行推广以纳入记忆限制。由于在存在记忆限制的LQG问题中估计和控制没有明确分离，因此将里卡蒂方程修改为部分可观测里卡蒂方程，这改进了估计以及控制。此外，通过将ML-POSC与局部LQG近似进行比较，我们证明了ML-POSC对于非LQG问题的有效性。
