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Dynamical Low-rank Approximations of Solutions to the Hamilton--Jacobi--Bellman Equation

Martin EigelReinhold SchneiderDavid Sommer

出版	Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021
URL	http://books.google.com.hk/books?id=q-L1zgEACAAJ&hl=&source=gbs_api

註釋

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