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

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Abstract

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.

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Authors and Affiliations

  1. Computer Network Information Center, Chinese Academy of Sciences, Beijing, 100190, China

    Yidong Chen & Zhonghua Lu

  2. University of Chinese Academy of Sciences, Beijing, 100190, China

    Yidong Chen & Zhonghua Lu

Authors
  1. Yidong Chen
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  2. Zhonghua Lu
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Corresponding authors

Correspondence to Yidong Chen or Zhonghua Lu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61873254.

This paper was recommended for publication by Editor ZHAO Yanlong.

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Chen, Y., Lu, Z. Tensor Decomposition and High-Performance Computing for Solving High-Dimensional Stochastic Control System Numerically. J Syst Sci Complex 35, 123–136 (2022). https://doi.org/10.1007/s11424-021-0126-0

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  • DOI: https://doi.org/10.1007/s11424-021-0126-0

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