  We consider a class of systems with time-varying parameters, which are
written as linear regressions with bounded disturbances. The task is to
estimate such parameters under the condition that the regressor is finitely
exciting (FE). Considering such a problem statement, a new robust method is
proposed to identify the time-varying parameters with bounded error, which
could be reduced to the limit by the adjustment of such method parameters. For
this purpose, the function of the system unknown parameters, which depends on
time, is expanded into a Taylor series in order to turn the considered problem
into the identification of the regression with piecewise-constant parameters.
This results in the increase of the dimensionality of the problem to be solved.
Then, the I-DREM procedure with exponential forgetting, resetting, and
normalization of the regressor, which has been proposed earlier by the authors,
is applied to the obtained regression. This allows one, in contrast to the
known solutions, to get the dimensionality of the problem back to the initial
one and provide the required exponential convergence of the parameter error to
a bounded set with adjustable bound under the condition that the regressor is
FE. In addition, this method guarantees that the parameter error is bounded
beyond the regressor excitation interval. The above properties are proved
analytically and shown via numerical simulations.
