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.
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© 2011 Springer Science+Business Media, LLC
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Kogut, P.I., Leugering, G.R. (2011). Suboptimal Control of Linear Steady-State Processes on Thin Periodic Structures with Mixed Boundary Controls. In: Optimal Control Problems for Partial Differential Equations on Reticulated Domains. Systems & Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8149-4_9
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DOI: https://doi.org/10.1007/978-0-8176-8149-4_9
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-8148-7
Online ISBN: 978-0-8176-8149-4
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