Optimization of the boundary control by shift or elastic force at one end of string in a sufficiently long arbitrary time

The problem of the boundary control optimization by shift or elastic force at one end of the string over a sufficiently long arbitrary time interval was solved by minimizing the $L_p$-norm of the derivative of control by shift or the $L_p$-norm of control by elastic force. Solution was established in an explicit analytical form which is valid for all $p\ge1$.