Minimax control of nonlinear evolution equations

Nikolaos S. Papageorgiou

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 1, page 39-56
  • ISSN: 0010-2628

Abstract

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In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.

How to cite

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Papageorgiou, Nikolaos S.. "Minimax control of nonlinear evolution equations." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 39-56. <http://eudml.org/doc/22078>.

@article{Papageorgiou1995,
abstract = {In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.},
author = {Papageorgiou, Nikolaos S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {minimax problem; optimal control; subdifferential; strong solution; Mosco convergence; obstacle problems; differential variational inequalities; evolution triple; compact embedding; monotone operator; -convergence; minimax optimization problem; saddle point; adjoint equation; duality theory; necessary conditions; Pontryagin maximum principle; nonlinear parametric optimal control},
language = {eng},
number = {1},
pages = {39-56},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Minimax control of nonlinear evolution equations},
url = {http://eudml.org/doc/22078},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Papageorgiou, Nikolaos S.
TI - Minimax control of nonlinear evolution equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 1
SP - 39
EP - 56
AB - In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.
LA - eng
KW - minimax problem; optimal control; subdifferential; strong solution; Mosco convergence; obstacle problems; differential variational inequalities; evolution triple; compact embedding; monotone operator; -convergence; minimax optimization problem; saddle point; adjoint equation; duality theory; necessary conditions; Pontryagin maximum principle; nonlinear parametric optimal control
UR - http://eudml.org/doc/22078
ER -

References

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  16. Zhikov V., Kozlov S., Oleinik O., Ngoan K., Averaging and G -convergence of differential operators, Russian Math. Surveys 34 (1979), 69-147. (1979) Zbl0421.35076MR0562800
  17. Ahmed N.U., Optimization and Identification of Systems Governed by Evolution Equations on Banach Spaces, Longman Publ. Co., Essex, United Kingdom, 1988. Zbl0645.93001MR0982263
  18. Ahmed N.U., Optimal control of infinite dimensional uncertain systems, J. Optim. Th. Appl. 80 (1994), 261-272. (1994) Zbl0798.49032MR1259659
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