Abstract: A
regular solution of the Problem 17 to and
can
be written in the form:The
second term of the second member is class if
but
only class in
the opposite case. The first term of the second member is always at least
absolutely continuous if u is integrable as compared to t,
because is
going to smooth irregularities of (more
or less following the regularity of G,
analytic or not notably).In
this paper, we show that the condition (4.7) defined by and m are constants and is the semi-group of class plays the fundamental role
in the study of the asymptotic behaviour of solutions in problems of dynamic
optimal control in the presence of perturbations.
Keywords and phrases: optimal control, semi-groups, behaviour asymptotic, regularity.
