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

Geometric Framework and Minimal Realizations of Nonlinear Systems on Fibre Bundle

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（Ｅ，）同构，（Ｆ，）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．

The definition of nonlinear control systems on fibre bundles proposed by Brockett and Willems in incomplete from the mathematical view. A new 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.