# On Controllability of an Elastic Ring

On Controllability of an Elastic Ring We study the exact controllability problem for a ring under stretching tension that varies in time. We are looking for a couple of forces, which drive the state solution to rest. We show that applying two forces is necessary for controllability and the ring is controllable in the time interval greater than the optical length of the string. We also explain why one force would not be enough to control the ring. We use the method of moments to reduce the controllability problem to a moment problem for the controlling forces. The solution of that problem is based on an auxiliary basis property result. Both method of moments and proof of the basis property are developed for the model with time-dependent parameters. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# On Controllability of an Elastic Ring

, Volume 60 (1) – Aug 1, 2009
33 pages

/lp/springer_journal/on-controllability-of-an-elastic-ring-SAfN1rqJIU
Publisher
Springer-Verlag
Subject
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-009-9064-2
Publisher site
See Article on Publisher Site

### Abstract

We study the exact controllability problem for a ring under stretching tension that varies in time. We are looking for a couple of forces, which drive the state solution to rest. We show that applying two forces is necessary for controllability and the ring is controllable in the time interval greater than the optical length of the string. We also explain why one force would not be enough to control the ring. We use the method of moments to reduce the controllability problem to a moment problem for the controlling forces. The solution of that problem is based on an auxiliary basis property result. Both method of moments and proof of the basis property are developed for the model with time-dependent parameters.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Aug 1, 2009

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