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). 2023 May 12;25(5):791. doi: 10.3390/e25050791.
Decentralized stochastic control (DSC) is a stochastic optimal control problem consisting of multiple controllers. DSC assumes that each controller is unable to accurately observe the target system and the other controllers. This setup results in two difficulties in DSC; one is that each controller has to memorize the infinite-dimensional observation history, which is not practical, because the memory of the actual controllers is limited. The other is that the reduction of infinite-dimensional sequential Bayesian estimation to finite-dimensional Kalman filter is impossible in general DSC, even for linear-quadratic-Gaussian (LQG) problems. In order to address these issues, we propose an alternative theoretical framework to DSC-memory-limited DSC (ML-DSC). ML-DSC explicitly formulates the finite-dimensional memories of the controllers. Each controller is jointly optimized to compress the infinite-dimensional observation history into the prescribed finite-dimensional memory and to determine the control based on it. Therefore, ML-DSC can be a practical formulation for actual memory-limited controllers. We demonstrate how ML-DSC works in the LQG problem. The conventional DSC cannot be solved except in the special LQG problems where the information the controllers have is independent or partially nested. We show that ML-DSC can be solved in more general LQG problems where the interaction among the controllers is not restricted.
分散随机控制（DSC）是一个由多个控制器组成的随机最优控制问题。DSC假设每个控制器无法准确观测目标系统和其他控制器。这种设置给DSC带来了两个困难；一是每个控制器必须记住无限维的观测历史，这并不实际，因为实际控制器的内存是有限的。另一个是，在一般的DSC中，即使对于线性二次高斯（LQG）问题，将无限维序贯贝叶斯估计简化为有限维卡尔曼滤波器也是不可能的。为了解决这些问题，我们提出了一个替代DSC的理论框架——内存受限的DSC（ML-DSC）。ML-DSC明确地构建了控制器的有限维内存。每个控制器通过联合优化，将无限维观测历史压缩到规定的有限维内存中，并基于此确定控制。因此，ML-DSC对于实际内存受限的控制器来说可以是一种实用的形式。我们展示了ML-DSC在LQG问题中是如何工作的。传统的DSC除了在控制器拥有的信息是独立或部分嵌套的特殊LQG问题中无法求解。我们表明，ML-DSC可以在更一般的LQG问题中求解，其中控制器之间的相互作用不受限制。
