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arXiv · 2111.14540

Dynamical low-rank approximations of solutions to the Hamilton-Jacobi-Bellman equation

Martin Eigel·Reinhold Schneider·David Sommer
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Abstract

We present a novel method to approximate optimal feedback laws for nonlinear optimal control based on low-rank tensor train (TT) decompositions. The approach is based on the Dirac-Frenkel variational principle with the modification that the optimisation uses an empirical risk. Compared to current state-of-the-art TT methods, our approach exhibits a greatly reduced computational burden while achieving comparable results. A rigorous description of the numerical scheme and demonstrations of its performance are provided.

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Martin Eigel, Reinhold Schneider, David Sommer. 2021-11-29. Dynamical low-rank approximations of solutions to the Hamilton-Jacobi-Bellman equation. https://arxiv.org/abs/2111.14540

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