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An optimal control for a flexible beam with shear force feedback

A flexible Euler-Bernoulli beam formulated by partial differential equations subject to the boundary shear force feedback is investigated in this paper. An abstract evolution equation corresponding to the beam system is established in an appropriate Hilbert space. A spectral analysis and semigroup generation of the system operator of the beam system are discussed. Finally, an optimal control with minimum norm is proposed and discusses. The existence and uniqueness of the optimal control are proposed and proved, and an approximation theorem is obtained in terms of semigroup methods of operators. A simulation result is shown in the paper.