Minimax optimal control problems. Numerical analysis of the finite horizon case
Silvia C. Di Marco; Roberto L. V. González
- Volume: 33, Issue: 1, page 23-54
- ISSN: 0764-583X
Access Full Article
topHow to cite
topDi Marco, Silvia C., and 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 33.1 (1999): 23-54. <http://eudml.org/doc/193913>.
@article{DiMarco1999,
author = {Di Marco, Silvia C., González, Roberto L. V.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {minimax optimal control problems; numerical examples; error bounds; finite difference method},
language = {eng},
number = {1},
pages = {23-54},
publisher = {Dunod},
title = {Minimax optimal control problems. Numerical analysis of the finite horizon case},
url = {http://eudml.org/doc/193913},
volume = {33},
year = {1999},
}
TY - JOUR
AU - Di Marco, Silvia C.
AU - González, Roberto L. V.
TI - Minimax optimal control problems. Numerical analysis of the finite horizon case
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 1
SP - 23
EP - 54
LA - eng
KW - minimax optimal control problems; numerical examples; error bounds; finite difference method
UR - http://eudml.org/doc/193913
ER -
References
top- [1] J.P. Aubin and A. Cellina, Differential inclusions. Springer-Verlag, New York (1984). Zbl0538.34007MR755330
- [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. Zbl0825.93979MR1269985
- [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. Zbl0822.65056MR1315000
- [4] E.N. Barron, Differential games with maximum cost. Nonlinear Analysis, Theory, Methods and Applications 14 (1990) 971-989. Zbl0708.90104MR1058417
- [5] E.N. Barron, The Pontryagin maximum principle for minimax problems of optimal control. Nonlinear Analysis, Theory, Methods and Applications 15 (1990) 1155-1165. Zbl0752.49013MR1082290
- [6] E.N. Barron, Averaging in Lagrange and minimax problems of optimal control. SIAM J. Contr. Opt. 31 (1930) 1630-1652. Zbl0791.49033MR1242220
- [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). Zbl0823.49002MR1289873
- [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. Zbl0691.49030MR1013311
- [9] E.N. Barron and R. Jensen, Relaxed minimax control. SIAM J. Contr. Opt. 33 (1995) 1028-1039. Zbl0824.49008MR1339052
- [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. Zbl0799.90139MR1237586
- [11] I. Capuzzo Dolcetta, On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming. Appl. Math. Optim. 10 (1983) 367-377. Zbl0582.49019MR713483
- [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. Zbl0674.49028MR1019113
- [13] I. Capuzzo Dolcetta and H. Ishii, Approximate solution of the Bellman equation of determmistic control theory. Appl. Math. Optim. 11 (1984) 161-181. MR743925
- [14] P.G. Ciarlet, Discrete maximum principle for finite-difference operators. Aequations Math. 4 (1970) 338-352. Zbl0198.14601MR292317
- [15] R. Dacorogna, Direct methods in the calculus of variations Springer-Verlag, Berlin (1987). Zbl0703.49001
- [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. Zbl0837.65066MR1355844
- [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). Zbl0229.90060MR421700
- [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. Zbl0563.49024MR777458
- [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). MR1154391
- [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. Zbl0747.65048MR1154391
- [23] G. Strang and G. Fix, An analysis of the finite element method Prentice-Hall, Englewood Cliffs, New Jersey (1973). Zbl0356.65096MR443377
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.