000			01367nam a2200169 a 4500
005			20260901030410.0
008			250101s2019 xx o 000 0 eng d
100	1		_aAlessandro Alla
245	1	0	_aA HJB-POD approach for the control of nonlinear PDEs on a tree structure
264		1	_barXiv _c2019
336			_atext
338			_aonline resource
520			_aThe 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		_aOpen access — freely available to read.
856	4	0	_uhttps://arxiv.org/pdf/1905.03395v2 _yRead the full paper (PDF)
942			_cERES
999			_c706 _d706