https://hal.inria.fr/hal-00800433Alla, AlessandroAlessandroAllaFalcone, MaurizioMaurizioFalconeUNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]An adaptive POD approximation method for the control of advection-diffusion equationsHAL CCSD2013[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Bouzat, EstelleSensitivity Analysis for Deterministic Controller Design - SADCO - - EC:FP7:PEOPLE2011-01-01 - 2014-12-31 - 264735 - VALID - Bredies, K.; Clason, C.; Kunisch, K.; von Winckel, G.2013-03-13 16:23:372022-11-25 19:04:092013-03-13 16:23:37enBook sections1We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic Programming approximation scheme for the corresponding evolutive Hamilton-Jacobi equation. We discuss several features regarding the adaptivity of the method, the role of error estimate indicators to choose a time subdivision of the problem and the computation of the basis functions. Some test problems are presented to illustrate the method.