HOMOGENIZATION OF QUASILINEAR OPTIMAL CONTROL PROBLEMS INVOLVING A THICK MULTILEVEL JUNCTION OF TYPE 3:2:1

作者：Durante Tiziana^*; Mel' nyk Taras A

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2012, 18(2): 583-610.

DOI：10.1051/cocv/2011107

• Homogenization
• quasilinear optimal control problem
• thick multilevel junction
• asymptotic behavior
• singular perturbation

We consider quasilinear optimal control problems involving a thick two-level junction Omega(epsilon) which consists of the junction body Omega(0) and a large number of thin cylinders with the cross-section of order O(epsilon(2)). 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 epsilon, alpha, beta and the thin cylinders from each level are epsilon-periodically alternated. Using the Buttazzo-Dal Maso abstract scheme for variational convergence of constrained minimization problems, the asymptotic analysis (as epsilon -%26gt; 0) of these problems are made for different values of alpha and beta 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.

• 出版日期2012-4