The paper addresses the problem of direct adaptive disturbance compensation in a linear system with known parameters and unmeasurable state. It is assumed that the amplitudes, frequencies, and phases of the external disturbance are a priori unknown, however the maximum number of harmonics is known. The solution to the problem is reduced to dynamic error model used to design an augmented error based adaptation algorithm with finite time convergence. The proposed adaptation algorithm is based on the prediction of dynamics of standard gradient-based algorithm and: preserves all properties of the gradient-based algorithm, including the convergence of the control error to zero irrespectively from the frequency properties of the regressor; ensures the finite time convergence of the parametric errors to zero under the persistent excitation condition or under the weaker condition of interval excitation; provides the alertness to slow or jumping variations of unknown parameters.

The problem of estimating the magnitude of faults in nonlinear dynamic systems in the presence of external disturbances is solved. The solution uses optimal control methods based on the transformation of the original system to a reduced linear system of a special type, sensitive to faults and insensitive to disturbances. Unlike sliding observers, traditionally used to solve this problem, the proposed approach allows avoiding high-frequency switching.