Ukrainian Mathematical Bulletin

Volume 3, Issue 1, 2006 pp. 131-144.

Control of a System with Elastic Components in the Non-resonance Case

Authors: Aleksander L. Zuyev
Author institution: Institute of Applied Mathematics and Mechanics of NAS of Ukraine, 74 R. Luxemburg Str., 83114, Donetsk, Ukraine Technical University of Ilmenau, P.O.B. 100565, D-98684 Ilmenau, Germany al_zv@mail.ru

Summary: We study the motion of a planar mechanical system that consists of a rigid body (carrier) and an arbitrary number of attached elastic beams. We find conditions for approximate controllability of such a model in terms of the spectrum of the corresponding homogeneous problem on oscillations of an elastic beam. We prove that the linear system is controllable with a scalar control, if no resonances occur. In the non-resonance case, we construct a feedback control that makes the trivial solution of the nonlinear system strongly asymptotically stable.

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