三阶时变离散系统的一致渐近稳定性  

Uniform asymptotic stability of 3rd-order time-variant discrete systems

作　　者：孙多青[1] 吴宏鑫[1] 

机构地区：[1]中国空间技术研究院北京控制工程研究所,36信箱北京100080

出　　处：《宇航学报》2004年第5期502-506,共5页Journal of Astronautics

基　　金：国家自然科学基金重点资助项目(60034010);国家自然科学基金资助项目(90205008);973计划资助项目(2002CB312205)

摘　　要：特征建模的方法为智能控制器设计和一些高阶对象进行低阶控制器设计提供了理论依据,特别是为大型空间挠性航天器的控制提供了一种有效的途径。但是,对于阶次和参数未知的高阶线性定常系统基于特征模型设计的自适应控制方案,其稳定性问题尚未完全解决,这一问题实际上归结为时变离散系统的稳定性问题。对于位置保持或位置跟踪控制,基于特征模型设计的自适应控制方案其稳定性问题即为三阶时变离散系统的稳定性问题,利用Lyapunov直接方法定量地给出了三阶线性时变离散系统和一类非线性三阶时变离散系统一致渐近稳定的判据,从而为基于特征建模设计适当的控制律以满足稳定性的要求提供了理论依据。The method on characteristic modelling lays a theoretical foundation for designs of intelligent controllers and using lower controller to control higher plant. Especially, the method provides a useful approach for the control of the flexible spacecraft in large space. However, for any linear time-invariant higher order plant with unknown parameter and order, the question of stability analysis of the adaptive control methods based on characteristic modelling is still an open question in general case, and this question is the stability of time-variant discrete systems. For the control of position keeping or position tracking, the stability of the adaptive control methods based on characteristic modelling is exactly the stability of 3rd-order time-variant discrete systems. Based on Lyapunov's direct method, this paper proposed quantitatively a criterion of the uniform asymptotic stability of 3rd-order linear time-variant discrete systems and a class of non-linear time-variant discrete systems. The criterion lays a theoretical foundation for the controller designs based on characteristic modelling so that the controllers can satisfy stability requirement.

关 键 词：挠性航天器 时变离散系统 渐近稳定性 特征建模 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O175.13[自动化与计算机技术—控制科学与工程]