Tensor Decomposition and High-Performance Computing for Solving High-Dimensional Stochastic Control System Numerically

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.