In this work we deal with the numerical solution of a Hamilton-Jacobi-Bellman (HJB) equation with infinitely many solutions. To compute the maximal solution - the optimal cost of the original optimal control problem - we present a complete discrete method based on the use of some finite elements and penalization techniques.
Keywords: multiple solutions, eikonal equation, singular optimal control problems, penalization methods, numerical approximation
@article{M2AN_2007__41_3_461_0, author = {Di Marco, Silvia C. and Gonz\'alez, Roberto L. V.}, title = {Numerical procedure to approximate a singular optimal control problem}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {461--484}, publisher = {EDP-Sciences}, volume = {41}, number = {3}, year = {2007}, doi = {10.1051/m2an:2007028}, mrnumber = {2355708}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an:2007028/} }
TY - JOUR AU - Di Marco, Silvia C. AU - González, Roberto L. V. TI - Numerical procedure to approximate a singular optimal control problem JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 461 EP - 484 VL - 41 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2007028/ DO - 10.1051/m2an:2007028 LA - en ID - M2AN_2007__41_3_461_0 ER -
%0 Journal Article %A Di Marco, Silvia C. %A González, Roberto L. V. %T Numerical procedure to approximate a singular optimal control problem %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 461-484 %V 41 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2007028/ %R 10.1051/m2an:2007028 %G en %F M2AN_2007__41_3_461_0
Di Marco, Silvia C.; González, Roberto L. V. Numerical procedure to approximate a singular optimal control problem. ESAIM: Modélisation mathématique et analyse numérique, Volume 41 (2007) no. 3, pp. 461-484. doi : 10.1051/m2an:2007028. http://archive.numdam.org/articles/10.1051/m2an:2007028/
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