Green's function approach in approximate controllability problems

A mathematical approach based on Green‘s function approach allowing to construct controls providing approximate controllability is suggested in the present paper. Representing the solution of governing system via Green’s formula and substituting it in prescribed terminal conditions, we obtain control functions providing approximate controllability of the system under study in explicit form. Choosing appropriate controls, we can provide required accuracy of approximation for prescribed conditions. Examples illustrating the procedure are described. Particularly, infinite string, controlled by a concentrated force, semi-infinite rod heated by a point heat source, finite rod heated from its boundary and parameter optimization for electrical circuit are considered. Results of computsations are brought.