In this paper, a necessary and sufficient condition for finite-time identification of a regression model, obtained using the dynamic regressor extension and mixing (DREM) method, is established. Estimators designed to satisfy transient and robust specifications via a time-varying gain are then proposed to have this condition as necessary and sufficient for their convergence to the true values when continuous functions are involved. These estimators are then used as a part of an adaptive control scheme, following a modular approach, to solve a tracking control problem for a nonlinear system in the strict feedback form with parametric and non-parametric uncertainty. It is shown that the necessary and sufficient condition can be expressed without using closed-loop signals, which allows attaining finite-time identification, exponential convergence to the tracking aim, and local/global robustness to non-parametric perturbations with minimal excitation conditions on the tracked trajectory. An example is developed to illustrate the main results.

在本文中，建立了使用动态回归量扩展和混合（DREM）方法获得的回归模型的有限时间识别的充分必要条件。然后提出通过时变增益满足瞬态和稳健规范的估计器，当涉及连续函数时，该条件对于它们收敛到真实值是必要和充分的。然后将这些估计器用作自适应控制方案的一部分，遵循模块化方法，以解决非线性系统具有参数和非参数不确定性的严格反馈形式。结果表明，可以在不使用闭环信号的情况下表达必要和充分条件，从而实现有限时间识别、对跟踪目标的指数收敛，以及在最小激励条件下对非参数扰动的局部/全局鲁棒性。跟踪的轨迹。开发了一个例子来说明主要结果。