Least regret control, virtual control and decomposition methods

@article{Lions2010,
abstract = { "Least regret control" consists in trying to find a control which "optimizes the situation" with the constraint of not making things too worse with respect to a known reference control, in presence of more or less significant perturbations. This notion was introduced in [7]. It is recalled on a simple example (an elliptic system, with distributed control and boundary perturbation) in Section 2. We show that the problem reduces to a standard optimal control problem for augmented state equations. On another hand, we have introduced in recent notes [9-12] the method of virtual control, aimed at the "decomposition of everything" (decomposition of the domain, of the operator, etc). An introduction to this method is presented, without a priori knowledge needed, in Sections 3 and 4, directly on the augmented state equations. For problems without control, or with "standard" control, numerical applications of the virtual control ideas have been given in the notes [9-12] and in the note [5]. One of the first systematic paper devoted to all kind of decomposition methods, including multicriteria, is a joint paper with A. Bensoussan and R. Temam, to whom this paper is dedicated, cf. [1]. },
author = {Lions, Jacques-Louis},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Control; least regret; domain decomposition; virtuel control.; least regret control; virtual control; second-order elliptic operator; quadratic functional; optimal control; algorithm},
language = {eng},
month = {3},
number = {2},
pages = {409-418},
publisher = {EDP Sciences},
title = {Least regret control, virtual control and decomposition methods},
url = {http://eudml.org/doc/197478},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Lions, Jacques-Louis
TI - Least regret control, virtual control and decomposition methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 2
SP - 409
EP - 418
AB - "Least regret control" consists in trying to find a control which "optimizes the situation" with the constraint of not making things too worse with respect to a known reference control, in presence of more or less significant perturbations. This notion was introduced in [7]. It is recalled on a simple example (an elliptic system, with distributed control and boundary perturbation) in Section 2. We show that the problem reduces to a standard optimal control problem for augmented state equations. On another hand, we have introduced in recent notes [9-12] the method of virtual control, aimed at the "decomposition of everything" (decomposition of the domain, of the operator, etc). An introduction to this method is presented, without a priori knowledge needed, in Sections 3 and 4, directly on the augmented state equations. For problems without control, or with "standard" control, numerical applications of the virtual control ideas have been given in the notes [9-12] and in the note [5]. One of the first systematic paper devoted to all kind of decomposition methods, including multicriteria, is a joint paper with A. Bensoussan and R. Temam, to whom this paper is dedicated, cf. [1].
LA - eng
KW - Control; least regret; domain decomposition; virtuel control.; least regret control; virtual control; second-order elliptic operator; quadratic functional; optimal control; algorithm
UR - http://eudml.org/doc/197478
ER -