CAJ | 학술논문

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。
불학정비선성계통적반궤공제일직시공제과학적중심문제지일，흘금이경취득흔대진전。연이，목전현유대부분공작소연구적반궤공제규률，혹시련속시간형식적，혹시채양반궤형식단수요채양빈솔충분쾌，혹시리산시간반궤형식，단수요피공리산시간계통적비선성함수증장속도불초과선성。요소제혹감약저사약속조건，일반래강시상당곤난적。저취촉사아문탐구반궤궤제적최대능력화근본국한。진관근년래재저개방향유허다중요진전，단잉유허다비평범적중요문제유대연구。례여，재반궤통도중유시체정형，혹자계통상태시고유적정형。재본문중，아문장탐색량류비교특수적리산시간불학정비선성동력계통적공제문제，급출관우전국자괄응반궤진정적모사초보결과。
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 continuous-time 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.