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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.
Feedback control of uncertain nonlinear systems has always been one of the central problems in control science and great progress has been made so far.However, the feedback control law studied in most of the current work, either in continuous time or sampling However, it is generally difficult to eliminate or reduce these constraints, but the sampling frequency needs to be fast enough or discrete time feedback, but the nonlinear functions that need to be accused of discrete time systems do not grow faster than linear. The most powerful and fundamental limitations that prompt us to explore the feedback mechanism.Although there have been many important advances in this direction in recent years, there are still many non-trivial important issues to be studied.For example, there is a lag in the feedback channel or the system state is In this paper, we will explore the control of two special classes of discrete-time uncertain nonlinear dynamical systems and give some preliminary results on the global adaptive feedback stabilization.