Computer aided modelling of optimal control

Dealing with the strict analytic modelling of non-homogeneous physical objects (strings, beams etc.) control leads to the trigonometric non-Fourier moment problem. The existence of solution of such a problem is still researched by many authors. The optimization of the solution is yet another problem. In current note, the algorithm for the solution with the least L²-norm is developed. The proposed algorithm allows to change an infinite system of moment equations into the linear one with only a finite number of equations. The idea of the approximating algorithm is based on the concept of quadratically close Hilbert spaces. This concept is the key point of approximation of optimal control. The note is concluded with the application of the proposed algorithm.