01367nam a2200169 a 4500 20260901030410.0 250101s2019 xx o 000 0 eng d Alessandro Alla A HJB-POD approach for the control of nonlinear PDEs on a tree structure arXiv 2019 text online resource 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. Open access — freely available to read. https://arxiv.org/pdf/1905.03395v2 Read the full paper (PDF) ERES 706 706 0 0 0 3 GEN MAIN MAIN SCICOMP 2026-09-01 0 YGE000967 2026-09-01 03:04:10 https://arxiv.org/pdf/1905.03395v2 2026-09-01 PAPER