Minimax optimal control problems. Numerical analysis of the finite horizon case
Di Marco, Silvia C. ; González, Roberto L. V.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 33 (1999), p. 23-54 / Harvested from Numdam
@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] J.P. Aubin and A. Cellina, Differential inclusions. Springer-Verlag, New York (1984). | MR 755330 | Zbl 0538.34007

[2] G. Barles, Ch. Daher and M. Romano, Optimal control on the L∞ norm of a diffusion process. SIAM J. Contr. Opt. 32 (1994) 612-634. | MR 1269985 | Zbl 0825.93979

[3] G. Barles, Ch. Daher and M. Romano, 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

[4] E.N. Barron, Differential games with maximum cost. Nonlinear Analysis, Theory, Methods and Applications 14 (1990) 971-989. | MR 1058417 | Zbl 0708.90104

[5] E.N. Barron, 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] E.N. Barron, Averaging in Lagrange and minimax problems of optimal control. SIAM J. Contr. Opt. 31 (1930) 1630-1652. | MR 1242220 | Zbl 0791.49033

[7] E.N. Barron, 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] E.N. Barron and H. Ishii, The Bellman equation for minimizing the maximum cost. Nonlinear Analysis, Theory, Methods and Applications 13 (1989) 1067-1090. | MR 1013311 | Zbl 0691.49030

[9] E.N. Barron and R. Jensen, Relaxed minimax control. SIAM J. Contr. Opt. 33 (1995) 1028-1039. | MR 1339052 | Zbl 0824.49008

[10] E.N. Barron, R. Jensen and J.L. Menaldi, Optimal control and differential games with measures. Nonlinear Analysis, Theory, Methods and Applications 21 (1993) 241-268. | MR 1237586 | Zbl 0799.90139

[11] I. Capuzzo Dolcetta, 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] I. Capuzzo Dolcetta and M. Falcone, 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

[13] I. Capuzzo Dolcetta and H. Ishii, Approximate solution of the Bellman equation of determmistic control theory. Appl. Math. Optim. 11 (1984) 161-181. | MR 743925

[14] P.G. Ciarlet, Discrete maximum principle for finite-difference operators. Aequations Math. 4 (1970) 338-352. | MR 292317 | Zbl 0198.14601

[15] R. Dacorogna, Direct methods in the calculus of variations Springer-Verlag, Berlin (1987). | Zbl 0703.49001

[16] S. C. Di Marco and R. L. V. Gonzalez, 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

[17] S. C. Di Marco and R. L. V. González, A minimax optimal control problem wih infinite horizon. Rapport de Recherche N°2945, INRIA, Rocquencourt (1996).

[18] A. Friedman, Differential games. Wiley-Interscience, New York (1971). | MR 421700 | Zbl 0229.90060

[19] R. L. V. González and E. Rofman, 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

[20] R.L.V. González and M.M. Tidball, On a discrete time approximation of the Hamilton-Jacobi equation of dynamic programming, Rapport de Recherche N°1375, INRIA, Rocquencourt (1990).

[21] R.L.V. González and M. M. Tidball, On the rate of convergence of fully discrete solutions of Hamilton-Jacobi equations, Rapport de Recherche N°1376, INRIA, Rocquencourt (1991). | MR 1154391

[22] R.L.V. González and M. M. Tidball, 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

[23] G. Strang and G. Fix, An analysis of the finite element method Prentice-Hall, Englewood Cliffs, New Jersey (1973). | MR 443377 | Zbl 0356.65096