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Numerical solution of a minimax ergodic optimal control problem
Author(s) -
S. Aragone Laura,
Soledad Aronna María,
Lotito Pablo A.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700956
Subject(s) - discretization , minimax , hamilton–jacobi–bellman equation , ergodic theory , mathematics , viscosity solution , optimal control , mathematical optimization , bellman equation , limit (mathematics) , mathematical analysis
In this work we consider an L ∞ minimax ergodic optimal control problem with cumulative cost. We approximate the cost function as a limit of evolutions problems. We present the associated Hamilton‐Jacobi‐Bellman equation and we prove that it has a unique solution in the viscosity sense. As this HJB equation is consistent with a numerical procedure, we use this discretization to obtain a procedure for the primitive problem. For the numerical solution of the ergodic version we need a perturbation of the instantaneous cost function. We give an appropriate selection of the discretization and penalization parameters to obtain discrete solutions that converge to the optimal cost. We present numerical results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)