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A system of a serially connected Euler-Bernoulli beam and its optimal energy control are studied by means of semigroup of linear operators in the present paper. The system is formulated by partial differential equations with the boundary conditions. The spectral analysis and semigroup generation of the system are discussed in the appropriate Hilbert spaces. Finally, an optimal energy control is proposed, and existence and uniqueness of the optimal control are demonstrated. Eventually, an approximation theorem is proved in terms of semigroup approach and geometric method. 

serially connected Euler-Bernoulli beam, optimal energy control, semigroup of linear operators.