关于自适应非线性镇定的某些结果

不确定非线性系统的反馈控制一直是控制科学的中心问题之一，迄今已经取得很大进展。然而，目前现有大部分工作所研究的反馈控制规律，或是连续时间形式的，或是采样反馈形式但需要采样频率充分快，或是离散时间反馈形式，但需要被控离散时间系统的非线性函数增长速度不超过线性。要消除或减弱这些约束条件，一般来讲是相当困难的。这就促使我们探究反馈机制的最大能力和根本局限。尽管近年来在这个方向有许多重要进展，但仍有许多非平凡的重要问题有待研究。例如，在反馈通道中有时滞情形，或者系统状态是高维的情形。在本文中，我们将探索两类比较特殊的离散时间不确定非线性动力系统的控制问题，给出关于全局自适应反馈镇定的某些初步结果。

Some results on adaptive nonlinear stabilization

Feedback control of uncertain nonlinear dynamical systems has been a central issue in control theory, and considerable progress has been made up to now. However, most of the existing works concern with either continuoustime feedback laws, or sampled-data feedback laws with sufficiently fast sampling, or with discrete-time feedback laws for parametric nonlinear systems with nonlinearities having a linear growth rate. Removing these constraints turns out to be quite difficult in general, which motivates the study of the maximum capability and fundamental limitations of the feedback mechanism. Although much effort has been made in this direction in recent years, many problems still remain open. For example, the case where there is a pure time-delay in the feedback channel or the case where the system state is of high dimension remains to be unexplored, which appears to be highly nontrivial. In this paper, we shall present some preliminary results on global adaptive nonlinear stabilization, by investigating two special classes of discrete-time uncertain nonlinear dynamical systems with delayed feedback and with two dimensional state signal, respectively.