"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 .
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
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. .