An optimal control problem for the second order linear differantial equations

In this thesis, an optimal control problem for the second order linear ordinary differential equation has been studied. The control function is at the right hand side of the equation. In the first chapter, a general information about the optimal control problems for the linear ordinary differential equations is given. In the second chapter, some mathematical definitions were presented. In the next chapter, the optimal control problem considered is presented. After proving necessary conditions for the existence and uniqueness of the optimal solution, the Frechet derivation of the cost functional can be found via the solution of the adjoint parabolic problem is obtained. Results are tested with a numerical example.