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)


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.


Optimal Control Problem Weak Convergence Variable Space Admissible Control Integral Identity 
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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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