SILVA, Luciano Cipriano da.; http://lattes.cnpq.br/9368773836942908; SILVA, Luciano Cipriano da.
Abstract:
We present hierarchic control to a parabolic system in a noncylindrical domain.
The hierarchic control is a problem that is how to bring in a fixed time, the solutions
of the equations of state we have, (these solutions depend on a functions called controls),
a state considered ideal, througha system of leading, independent control, and
followers, the leader controls dependents. We start by making a transformation of the
original problem to an equivalent cylindrical domain, then do the hierarchic control of
this problem. We use the strategy Stackelberg-Nash, a process in which each leader’s
choice, look for followers to satisfy a minimization problem, the solution of this problem
form what we call the Nash equilibrium, solved this problem, work to prove that
the approximately system is controllable using the leader. We further resolve to a of
optimality for followers.