https://hal.inria.fr/hal-01068295Alla, AlessandroAlessandroAllaFalcone, MaurizioMaurizioFalconeUniversità degli Studi di Roma "La Sapienza" = Sapienza University [Rome]Kalise, DanteDanteKaliseRICAM - Johann Radon Institute for Computational and Applied Mathematics - OeAW - Austrian Academy of SciencesAn Efficient Policy Iteration Algorithm for Dynamic Programming EquationsHAL CCSD2015[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]Bouzat, EstelleSensitivity Analysis for Deterministic Controller Design - SADCO - - EC:FP7:PEOPLE2011-01-01 - 2014-12-31 - 264735 - VALID - 2014-09-25 13:47:282021-11-03 14:18:082014-09-25 13:47:28enJournal articles10.1137/1309322841We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear convergence in many relevant cases provided the initial guess is sufficiently close to the solution. In many cases, this limitation degenerates into a behavior similar to a value iteration method, with an increased computation time. The new scheme circumvents this problem by combining the advantages of both algorithms with an efficient coupling. The method starts with a value iteration phase and then switches to a policy iteration procedure when a certain error threshold is reached. A delicate point is to determine this threshold in order to avoid cumbersome computation with the value iteration and, at the same time, to be reasonably sure that the policy iteration method will finally converge to the optimal solution. We analyze the methods and efficient coupling in a number of examples in dimension two, three and four illustrating its properties.