Exact boundary controllability and feedback stabilization for a multi-layer Rao-Nakra beam

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Ozer, Ahmet Ozkan
Iowa State University; Digital Repository @ Iowa State University
Boundary control; Exact controllability; Ingham's theorem; Multipliers method; Rayleigh beam; Sandwich beam
thesis / dissertation description
We prove exact boundary controllability for the Rayleigh beam equation with a single boundary control active at one end of the beam. This result is used to prove exact boundary controllability of the multilayer Rao-Nakra beam, which contains the Rayleigh beam as one of its component equations. We consider all combinations of clamped and hinged boundary conditions. In each case, exact controllability is obtained on the space of optimal regularity. We also obtain corresponding uniqueness and exact observability results for the dual observed system. Then we are able to obtain exponential stability of the multilayer Rao-Nakra beam system using an appropriate boundary feedback. We also formulate an abstract version of the closely related Mead-Marcus sandwich beam model and prove its boundary controllability using the multipliers technique.