We consider quasilinear optimal control problems involving a thick two-level junction
Ωε which consists of the junction body
Ω0 and a large number of thin cylinders with the
cross-section of order 𝒪(ε2). The thin cylinders
are divided into two levels depending on the geometrical characteristics, the quasilinear
boundary conditions and controls given on their lateral surfaces and bases respectively.
In addition, the quasilinear boundary conditions depend on parameters ε, α,
β and the thin cylinders from each level are ε-periodically
alternated. Using the Buttazzo–Dal Maso abstract scheme for variational convergence of
constrained minimization problems, the asymptotic analysis (as ε → 0) of
these problems are made for different values of α and β
and different kinds of controls. We have showed that there are three qualitatively
different cases. Application for an optimal control problem involving a thick one-level
junction with cascade controls is presented as well.