A HJB-POD approach for the control of nonlinear PDEs on a tree structure (Record no. 706)

000 -LEADER
fixed length control field 01367nam a2200169 a 4500
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20260901030410.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 250101s2019 xx o 000 0 eng d
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Alessandro Alla
245 10 - TITLE STATEMENT
Title A HJB-POD approach for the control of nonlinear PDEs on a tree structure
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Name of producer, publisher, distributor, manufacturer arXiv
Date of production, publication, distribution, manufacture, or copyright notice 2019
336 ## - CONTENT TYPE
Content type term text
338 ## - CARRIER TYPE
Carrier type term online resource
520 ## - SUMMARY, ETC.
Summary, etc. The Dynamic Programming approach allows to compute a feedback control for nonlinear problems, but suffers from the curse of dimensionality. The computation of the control relies on the resolution of a nonlinear PDE, the Hamilton-Jacobi-Bellman equation, with the same dimension of the original problem. Recently, a new numerical method to compute the value function on a tree structure has been introduced. The method allows to work without a structured grid and avoids any interpolation. Here, we aim to test the algorithm for nonlinear two dimensional PDEs. We apply model order reduction to decrease the computational complexity since the tree structure algorithm requires to solve many PDEs. Furthermore, we prove an error estimate which guarantees the convergence of the proposed method. Finally, we show efficiency of the method through numerical tests.
506 0# - RESTRICTIONS ON ACCESS NOTE
Terms governing access Open access — freely available to read.
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://arxiv.org/pdf/1905.03395v2">https://arxiv.org/pdf/1905.03395v2</a>
Link text Read the full paper (PDF)
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      Available online General Yegates University Library Yegates University Library Science and Computing 09/01/2026   YGE000967 09/01/2026 https://arxiv.org/pdf/1905.03395v2 09/01/2026 Research paper — read online