Minimax optimal control problems. Numerical analysis of the finite horizon case

Silvia C. Di Marco; Roberto L.V. González

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 33, Issue: 1, page 23-54
  • ISSN: 0764-583X

Abstract

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In this paper we consider the numerical computation of the optimal cost function associated to the problem that consists in finding the minimum of the maximum of a scalar functional on a trajectory. We present an approximation method for the numerical solution which employs both discretization on time and on spatial variables. In this way, we obtain a fully discrete problem that has unique solution. We give an optimal estimate for the error between the approximated solution and the optimal cost function of the original problem. Also, numerical examples are presented.

How to cite

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Di 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 33.1 (2010): 23-54. <http://eudml.org/doc/197400>.

@article{DiMarco2010,
abstract = { In this paper we consider the numerical computation of the optimal cost function associated to the problem that consists in finding the minimum of the maximum of a scalar functional on a trajectory. We present an approximation method for the numerical solution which employs both discretization on time and on spatial variables. In this way, we obtain a fully discrete problem that has unique solution. We give an optimal estimate for the error between the approximated solution and the optimal cost function of the original problem. Also, numerical examples are presented. },
author = {Di Marco, Silvia C., González, Roberto L.V.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {minimax problems; optimal cost function; discrete maximum principle; fully discrete solution.; minimax optimal control problems; numerical examples; error bounds; finite difference method},
language = {eng},
month = {3},
number = {1},
pages = {23-54},
publisher = {EDP Sciences},
title = {Minimax optimal control problems. Numerical analysis of the finite horizon case},
url = {http://eudml.org/doc/197400},
volume = {33},
year = {2010},
}

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
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 1
SP - 23
EP - 54
AB - In this paper we consider the numerical computation of the optimal cost function associated to the problem that consists in finding the minimum of the maximum of a scalar functional on a trajectory. We present an approximation method for the numerical solution which employs both discretization on time and on spatial variables. In this way, we obtain a fully discrete problem that has unique solution. We give an optimal estimate for the error between the approximated solution and the optimal cost function of the original problem. Also, numerical examples are presented.
LA - eng
KW - minimax problems; optimal cost function; discrete maximum principle; fully discrete solution.; minimax optimal control problems; numerical examples; error bounds; finite difference method
UR - http://eudml.org/doc/197400
ER -

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