An adaptive control is designed for a multidimensional system with unknown constant coefficients under bounded polyharmonic disturbances containing an infinite number of harmonics of unknown amplitudes and frequencies. It uses a very small test signal. The control aim is to ensure given bounds for the forced oscillations in the output of the system and controller. Adaptation is based on finite-frequency identification of the system and a closed-loop system. By way of example, an adaptive control of a real physical system is given.