The influence of an external loading on nonlinear dynamic processes in a layer having a di-atomic crystalline structure is studied. An asymptotic procedure is developed to transform the solution of the initial two-dimensional problem to the solution to the coupled one-dimensional nonlinear equations for longitudinal macrostrains and variations in the microstructure. It is shown that an external loading on the lateral surface of the layer can play the role of a feedback control supporting the stable propagation of localized strain waves. The weakly nonlinear case is considered to obtain a new single governing equation for longitudinal strains.