Exact controllability of a Rayleigh beam with a single boundary control
Exact controllability of a Rayleigh beam with a single boundary control
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具有单一边界控制的瑞利光束的精确可控性
DOI：
10.1007/s00498-011-0069-4
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
S. Hansen
中科院分区：
文献类型：
--
作者：
A. Özer;S. 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 L2(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.
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 L2(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.