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arXiv · 1908.01533

Tensor Decomposition Methods for High-dimensional Hamilton-Jacobi-Bellman Equations

Sergey Dolgov·Dante Kalise·Karl Kunisch
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Abstract

A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The method combines a tensor train approximation for the value function together with a Newton-like iterative method for the solution of the resulting nonlinear system. The tensor approximation leads to a polynomial scaling with respect to the dimension, partially circumventing the curse of dimensionality. A convergence analysis for the linear-quadratic case is presented. For nonlinear dynamics, the effectiveness of the high-dimensional control synthesis method is assessed in the optimal feedback stabilization of the Allen-Cahn and Fokker-Planck equations with a hundred of variables.

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Sergey Dolgov, Dante Kalise, Karl Kunisch. 2019-08-05. Tensor Decomposition Methods for High-dimensional Hamilton-Jacobi-Bellman Equations. https://arxiv.org/abs/1908.01533

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