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Boundary controllability of nonlinear beams to bounded states

Published online by Cambridge University Press:  14 November 2011

J. E. Lagnese
J. E. Lagnese
Affiliation:
Department of Mathematics, Georgetown University, Washington, DC 20057, U.S.A
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Synopsis

Considered is a nonlinear model which describes the dynamic behaviour of the not necessarily small longitudinal and transverse displacements of a thin, cantilevered beam. The motion of the beam is driven by a bending moment, an axial force and a vertical shear force that act at the free end of the beam. The main goal is to describe the reachable set of the system, that is, the set of all states that can be reached by varying the end forces within a certain set of admissible controls.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 119 , Issue 1-2 , 1991 , pp. 63 - 72
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

1Chewning, W. C.. Controllability of the nonlinear wave equation in several space variables. SIAM J. Control 14 (1976), 19–25.CrossRefGoogle Scholar
2Fattorini, H.. Local controllability of a nonlinear wave equation. Math. Systems Theory 9 (1975), 35–40.CrossRefGoogle Scholar
3Lagnese, J. E.. Boundary Stabilization of Thin Plates, Studies in Applied Mathematics 10 (Philadelphia: SIAM Publications, 1989).CrossRefGoogle Scholar
4Lagnese, J. E.. The reachability problem for thermoelastic plates. Arch. Rational Mech. Anal. 112 (1990), 223–267.CrossRefGoogle Scholar
5Lagnese, J. E.. Recent progress in exact boundary controllability and uniform stabilizability of thin beams and plates. In Distributed Parameter Control Systems: New Trends and Applications, ed. , Goong Chen (New York: Marcel Dekker, 1990), 61–111.Google Scholar
6Lagnese, J. E. and Leugering, G.. Uniform stabilization of a nonlinear beam by nonlinear boundary feedback. J. Differential Equations 90 (1991).Google Scholar
7Lagnese, J. E. and Lions, J.-L.. Modelling, Analysis and Control of Thin Plates, Collection RMA 6 (Paris: Masson, 1988).Google Scholar
8Lasiecka, I. and Triggiani, R.. Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems. Proc. 28th IEEE Conf. on Decision and Control, Tampa, FL, December, 1989, pp. 2291–2294.Google Scholar
9Lions, J.-L.. Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués. Tome 1, Contrôlabilité Exacte, Recherches en Matheématiques Appliquées 8 (Paris: Masson, 1988).Google Scholar
10Markus, L.. Controllability of nonlinear processes. SIAM J. Control 3 (1965), 78–90.Google Scholar
11Zuazua, E.. Exact controllability of semilinear wave equations. Proceedings 27th IEEE CDC, Austin, TX, 1988, pp. 1265–1268.Google Scholar