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

I-DREM MRAC with Time-Varying Adaptation Rate & No A Priori Knowledge of Control Input Matrix Sign to Relax PE Condition