  The paper considers the observer synthesis for nonlinear, time-varying plants
with uncertain parameters under multiharmonic disturbance. It is assumed that
the relative degree of the plant is known, the regressor linearly depends on
the state vector and may have a nonlinear relationship with the output signal.
The proposed solution consists of three steps. Initially, an unknown input
state observer is synthesized. This observer, however, necessitates the
measurement of output derivatives equal to the plant's relative degree. To
relax this limitation, an alternative representation of the observer is
introduced. Further, based on this observer, the unknown parameters and
disturbances are reconstructed using an autoregression model and the dynamic
regressor extension and mixing (DREM) approach. This approach allows the
estimates to be obtained in a finite time. Finally, based on these estimates,
an observer has been constructed that does not require measurements of the
output derivatives. The effectiveness and efficiency of this solution are
demonstrated through a computer simulation.
