In this paper, a dynamic regressor extension and mixed estimator is proposed with finite-time convergence and freedom to choose its time-varying adaptation gain and its derivation order. This freedom is exploited to enhance the transient and robustness performance of the estimation by analytically establishing the effects of both variables. The proposed estimator is used to design adaptive controllers and observers for nonlinear systems, which exhibit exponential order of convergence at an arbitrary rate of decay with robust and improved transient properties. These results are illustrated in a tracking control of nonlinear systems with parametric uncertainty.

提出了一种具有有限时间收敛性和自由度的动态回归扩展与混合估计量，以选择其随时间变化的自适应增益及其推导阶数。通过分析建立两个变量的影响，利用这种自由度来增强估计的瞬态和鲁棒性。所提出的估计器用于设计非线性系统的自适应控制器和观测器，这些控制器和观测器在任意衰减率下均具有指数级收敛性，并且具有鲁棒且经过改进的瞬态特性。在具有参数不确定性的非线性系统的跟踪控制中说明了这些结果。