纤维丛上一般非线性控制系统的几何框架及其最小实现理论<sup>*</sup>

慕小武

纤维丛上一般非线性控制系统的几何框架及其最小实现理论^*

慕小武

郑州大学系统科学与数学系, 郑州 450052

基金项目: * 国家自然科学青年基金,河南省自然科学资金

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出版历程
- 收稿日期: 1996-03-20
- 刊出日期: 1996-10-15

Geometric Framework and Minimal Realizations of Nonlinear Systems on Fibre Bundle

Mu Xiaowu

Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P. R. China

摘要

摘要: 本文探讨正确建立一般非线性控制系统纤维丛框架的途径,并研究了纤维丛上系统的最小实现理论。我们在本文中通过引进(F,φ)同构,(F,φ)同态,强等价等新概念,实质上拓广了H.J.Sussmann所发展的非线性系统实现理论的经典概念和结果,并证明了纤维丛上的一般非线性系统的最小实现唯一性定理。
- 纤维丛 /
- 能观性 /
- 能控性 /
- 最小实现
Abstract: The definition of nonlinear control sysms on fibre bundles proposed by Brockett and Willems is incomplete from the mathematical view geometric framework is proposed and a minimal realization theory is developed for nonlinear control systems on fibre bundles which is elaborated as a natural generalization of Sussmann's theory and differs essentially from Van der Schaft's approach. Limitations of realization theory given by Van der Schaft are also discussed.
- fibre bundle /
- controllability /
- observability /
- minimality

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参考文献(16)

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