On optimal control of the initial velocity of an Euler-Bernoulli beam system

In this study, we consider an optimal control problem for Euler-Bernoulli beam equation. The initial velocity of the system is given by function. We give sufficient conditions existence a unique solution hyperbolic and prove that considered exists unique. After obtaining Frechet derivative cost functional via adjoint problem, also iteration algorithm numerical using Gradient method. Finally, furnish some examples to demonstrate effectiveness result obtained.