Suboptimal Control of Linear Steady-State Processes on Thin Periodic Structures with Mixed Boundary Controls
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.
KeywordsOptimal Control Problem Weak Convergence Variable Space Admissible Control Integral Identity
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