  The known dynamic regressor extension and mixing method (DREM) is combined
with the proposed filter of a new type, which uses the integration operation,
and the recursive least-squares method to develop the new I-DREM model
reference adaptive control (MRAC) system. It does not require a priori
knowledge of the sign or the elements values of the control input matrix of the
plant. It also provides the exponential convergence of the adaptation process
(with the automatically adjustable adaptation rate) without the regressor
persistent excitation. Such control system allows to solve three actual
problems of the adaptive control: 1) to provide the exponential convergence of
the controller parameter error under the condition of the regressor initial
excitation, 2) to make such convergence monotonic, 3) to calculate the
adaptation rate online according to the current regressor value. Some numerical
experiments are conducted to demonstrate the effectiveness of the proposed
method.
