@article{M2AN_1999__33_1_23_0, author = {Di Marco, Silvia C. and Gonz\'alez, Roberto L. V.}, title = {Minimax optimal control problems. Numerical analysis of the finite horizon case}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {33}, year = {1999}, pages = {23-54}, mrnumber = {1685742}, zbl = {0918.65049}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_1999__33_1_23_0} }
Di Marco, Silvia C.; González, Roberto L. V. Minimax optimal control problems. Numerical analysis of the finite horizon case. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 33 (1999) pp. 23-54. http://gdmltest.u-ga.fr/item/M2AN_1999__33_1_23_0/
[1] Differential inclusions. Springer-Verlag, New York (1984). | MR 755330 | Zbl 0538.34007
and ,[2] Optimal control on the L∞ norm of a diffusion process. SIAM J. Contr. Opt. 32 (1994) 612-634. | MR 1269985 | Zbl 0825.93979
, and ,[3] Convergence of numerical schemes for parabolic equations arising in finace theory. Math. Models Met. Appl. Sci. 5 (1995) 125-143. | MR 1315000 | Zbl 0822.65056
, and ,[4] Differential games with maximum cost. Nonlinear Analysis, Theory, Methods and Applications 14 (1990) 971-989. | MR 1058417 | Zbl 0708.90104
,[5] The Pontryagin maximum principle for minimax problems of optimal control. Nonlinear Analysis, Theory, Methods and Applications 15 (1990) 1155-1165. | MR 1082290 | Zbl 0752.49013
,[6] Averaging in Lagrange and minimax problems of optimal control. SIAM J. Contr. Opt. 31 (1930) 1630-1652. | MR 1242220 | Zbl 0791.49033
,[7] Optimal control and calculus of variations in L∞, in Optimal Control in Differential Equations. N.H. Pavel and Marcel Dekker Eds., New York (1994). | MR 1289873 | Zbl 0823.49002
,[8] The Bellman equation for minimizing the maximum cost. Nonlinear Analysis, Theory, Methods and Applications 13 (1989) 1067-1090. | MR 1013311 | Zbl 0691.49030
and ,[9] Relaxed minimax control. SIAM J. Contr. Opt. 33 (1995) 1028-1039. | MR 1339052 | Zbl 0824.49008
and ,[10] Optimal control and differential games with measures. Nonlinear Analysis, Theory, Methods and Applications 21 (1993) 241-268. | MR 1237586 | Zbl 0799.90139
, and ,[11] On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming. Appl. Math. Optim. 10 (1983) 367-377. | MR 713483 | Zbl 0582.49019
,[12] Discrete dynamic programming and viscosity solutions of the Bellman equation. Ann. Inst. Henry Poincaré. Anal. Non-lin. 6 (1989) 161-184. | Numdam | MR 1019113 | Zbl 0674.49028
and ,[13] Approximate solution of the Bellman equation of determmistic control theory. Appl. Math. Optim. 11 (1984) 161-181. | MR 743925
and ,[14] Discrete maximum principle for finite-difference operators. Aequations Math. 4 (1970) 338-352. | MR 292317 | Zbl 0198.14601
,[15] Direct methods in the calculus of variations Springer-Verlag, Berlin (1987). | Zbl 0703.49001
,[16] Une procedure numérique pour la minimisation du coût maximum. C. R. Acad. Sci. Pans, Série I 321 (1995) 869-874. | MR 1355844 | Zbl 0837.65066
and ,[17] A minimax optimal control problem wih infinite horizon. Rapport de Recherche N°2945, INRIA, Rocquencourt (1996).
and ,[18] Differential games. Wiley-Interscience, New York (1971). | MR 421700 | Zbl 0229.90060
,[19] On deterministic control problems: An approximation procedure for the optimal cost, Parts 1 and 2, SIAM J. Contr. Opt. 23 (1985) 242-285. | MR 777458 | Zbl 0563.49024
and ,[20] On a discrete time approximation of the Hamilton-Jacobi equation of dynamic programming, Rapport de Recherche N°1375, INRIA, Rocquencourt (1990).
and ,[21] On the rate of convergence of fully discrete solutions of Hamilton-Jacobi equations, Rapport de Recherche N°1376, INRIA, Rocquencourt (1991). | MR 1154391
and ,[22] Sur l'ordre de convergence des solutions discrétisées en temps et en espace de l'équation de Hamilton-Jacobi, C. R. Acad. Sci., Paris, Série I 314 (1992) 479-482. | MR 1154391 | Zbl 0747.65048
and ,[23] An analysis of the finite element method Prentice-Hall, Englewood Cliffs, New Jersey (1973). | MR 443377 | Zbl 0356.65096
and ,