Abstract
In this work we present a numerical procedure for the ergodic optimal minimax control problem. Restricting the development to the case with relaxed controls and using a perturbation of the instantaneous cost function, we obtain discrete solutions U k ε that converge to the optimal relaxed cost U when the relation ship between the parameters of discretization k and penalization ε is an appropriate one.
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Alvarez, O., & Barron, E. N. (2000). Ergodic control in L ∞. Set-Valued Analysis, 8(1, 2), 51–69.
Di Marco, S. C., & González, R. L. V. (1999a). Relaxation of minimax optimal control problems with infinite horizon. Journal of Optimization Theory and Applications, 101(2), 285–306.
Di Marco, S. C., & González, R. L. V. (1999b). Minimax optimal control problems. Numerical analysis of the finite horizon case. Mathematical Modelling and Numerical Analysis, 33(1), 23–54.
González, R. L. V., & Aragone, L. S. (2000). A Bellman’s equation for minimizing the maximum cost. Indian Journal of Pure Applied Mathematics, 31(12), 1621–1632.
Friedman, A. (1971). Differential games. New York: Wiley.
Lions, P. L. (1985). Newman type boundary conditions for Hamilton-Jacobi equations. Duke Mathematical Journal, 5(3), 793–820.
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This paper aims to be a tribute to Prof. Roberto L.V. González who died after we finished this work.
This paper was supported by grant PIP 5379 CONICET.
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Aragone, L.S., González, R.L.V. & Reyero, G.F. Penalization techniques in L ∞ optimization problems with unbounded horizon. Ann Oper Res 164, 17–27 (2008). https://doi.org/10.1007/s10479-007-0259-0
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DOI: https://doi.org/10.1007/s10479-007-0259-0