Numerical solution of a minimax ergodic optimal control problem,

ARAGONE L. S.; ARONNA, M. S.; LOTITO P. A

proceedings in Applied Mathematics and Mechanics

Wiley

Lugar: Weinheim; Año: 2007 vol. 7 p. 1040311 - 1040312

1617-7061

In this work we consider an L-infinity min-max 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.