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

2021/11/29 by Martin Eigel, Eigel, Martin, Reinhold Schneider +3 · 2 citations
Mathematics · #15A69 #49L20 #49M37 #93-08 #93B52 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:15A69 #msc:49L20 #msc:49M37 #msc:93-08 #msc:93B52

paper · pdf · doi:10.48550/arxiv.2111.14540

arxiv created 2021/11/29 · arxiv updated 2021/11/30

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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