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Dynamical low‐rank approximations of solutions to the Hamilton–Jacobi–Bellman equation
Author(s) -
Eigel Martin,
Schneider Reinhold,
Sommer David
Publication year - 2023
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2463
Subject(s) - mathematics , rank (graph theory) , tensor (intrinsic definition) , optimal control , nonlinear system , scheme (mathematics) , dirac (video compression format) , state (computer science) , bellman equation , current (fluid) , approximations of π , mathematical optimization , mathematical analysis , pure mathematics , algorithm , quantum mechanics , combinatorics , physics , electrical engineering , neutrino , engineering
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 optimization 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.