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Suboptimal Control of Linear Steady-State Processes on Thin Periodic Structures with Mixed Boundary Controls

  • Peter I. Kogut
  • Günter R. Leugering
Part of the Systems & Control: Foundations & Applications book series (SCFA)

Abstract

Our main interest in this chapter is in approximate solutions to a class of optimal control problems (OCPs) on thin periodic structures. Typically, thin structures are characterized by two properties: periodicity and small thickness of the material. More precisely, we suppose that the geometry of such structures depends on two small parameters, ε and h(ε), related to each other by the assumption h(ε)→0 as ε→0 and determining the cell of periodicity and thickness of constituting components, respectively. This is in contrast to the periodically perforated domain for which h=h(ε)→const∈(0,1] as ε→0. In view of this, it should be noted that the asymptotic analysis of boundary value problems in a perforated domain with small holes (without controls) has been intensively studied by many authors.

Keywords

Optimal Control Problem Weak Convergence Variable Space Admissible Control Integral Identity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics and Mechanics, Department of Differential EquationsOles Honchar Dnipropetrovsk National UniversityDnipropetrovskUkraine
  2. 2.Department of Mathematics, Chair of Applied Mathematics IIFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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