A highly nonlinear system of acoustic and optical oscillations in a complex crystalline lattice consisting of two sublattices is analyzed. The system is obtained as a generalization of the linear Carman-Born-Kun Huang theory. Large displacements of atoms up to structure stability loss and restructuring are admitted. It is shown that the system has nontrivial solutions describing movements of fronts, emergence of periodic structures and defects. Strong interaction of acoustic and optical modes of oscillations for media without center of symmetry, energy exchange between modes and excitation of the optical mode by means of torque applied to the ends of the lattice (rod) are examined. Control algorithm based on speed-gradient method is proposed. Simulation results demonstrate that application of control may allow to eliminate or reduce influence of initial conditions