The paper presents a numerical method for solving a class of high-dimensional stochastic control systems based on tensor decomposition and parallel computing. The HJB solution provides a globally optimal controller to the associated dynamical system. Variable substitution is used to simplify the nonlinear HJB equation. The curse of dimensionality is avoided by representing the HJB equation using separated representation. Alternating least squares (ALS) is used to reduced the separation rank. The experiment is conducted and the numerical solution is obtained. A high-performance algorithm is designed to reduce the separation rank in the parallel environment, solving the high-dimensional HJB equation with high efficiency.

本文提出了一种基于张量分解和并行计算的高维随机控制系统的数值方法。HJB解决方案为关联的动力学系统提供了全局最优控制器。变量替换用于简化非线性HJB方程。通过使用分离的表示形式表示HJB方程，可以避免维数的诅咒。交替最小二乘（ALS）用于减小分离等级。进行了实验并获得了数值解。设计了一种高性能算法来降低并行环境中的分离秩，从而高效地解决了高维HJB方程。