Аннотация:This paper provides a modified method that allows one to solve the problem of the optimal boundary controls μ(t) and ν(t) of displacements at two ends of a string for a large time interval T = 2ln, where n = 1, 2, 3, … It should be noted that the minimization was made in the space Lp with p ≥ 1. Besides, it was found that the derivatives of above-mentioned functions are 2l-periodic functions.