caa a22 4500 445868589 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00498-011-0069-4 doi (NATIONALLICENCE)springer-10.1007/s00498-011-0069-4 Exact controllability of a Rayleigh beam with a single boundary control [Elektronische Daten] [A. Ozkan Ozer, Scott Hansen] We prove exact boundary controllability for the Rayleigh beam equation $${\varphi_{tt} -\alpha\varphi_{ttxx} + A\varphi_{xxxx} = 0, 0 < x < l, t > 0}$$ with a single boundary control active at one end of the beam. We consider all combinations of clamped and hinged boundary conditions with the control applied to either the moment $${\varphi_{xx}(l, t)}$$ or the rotation angle $${\varphi_{x}(l, t)}$$ at an end of the beam. In each case, exact controllability is obtained on the space of optimal regularity for L 2(0, T) controls for $${T > 2l\sqrt{\frac{\alpha}{A}}}$$ . In certain cases, e.g., the clamped case, the optimal regularity space involves a quotient in the velocity component. In other cases, where the regularity for the observed problem is below the energy level, a quotient space may arise in solutions of the observed problem. Springer-Verlag London Limited, 2011 Rayleigh beam nationallicence Boundary control nationallicence Exact controllability nationallicence Kirchhoff plate nationallicence Continuous observability nationallicence Ingham's theorem nationallicence Ozkan Ozer A. Department of Mathematics, Iowa State University, 50011, Ames, IA, USA aut Hansen Scott Department of Mathematics, Iowa State University, 50011, Ames, IA, USA aut Mathematics of Control, Signals, and Systems Springer-Verlag 23/1-3(2011-12-01), 199-222 0932-4194 23:1-3<199 2011 23 498 https://doi.org/10.1007/s00498-011-0069-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00498-011-0069-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ozkan Ozer A. Department of Mathematics, Iowa State University, 50011, Ames, IA, USA aut NATIONALLICENCE 700 1- Hansen Scott Department of Mathematics, Iowa State University, 50011, Ames, IA, USA aut NATIONALLICENCE 773 0- Mathematics of Control, Signals, and Systems Springer-Verlag 23/1-3(2011-12-01), 199-222 0932-4194 23:1-3<199 2011 23 498 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer