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		Yinhe Wang,Zhiyuan Li,Siying Zhang.[en_title][J].Control Theory and Technology,2004,2(3):267~275.[Copy]

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YinheWang,ZhiyuanLi,SiyingZhang
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Received:February 13, 2004Revised:August 03, 2004

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Approximation property of partition of unity and its applications

Yinhe Wang, Zhiyuan Li,Siying Zhang

(Science College, Shantou University, 515063 Shantou Guangdong, China;Department of Mathematics, Inner Mongolia Normal University, 010022 Huhhot Inner Mongolia, China; Department of Automatic Control, Northeastern University, 110006 Shenyang Liaoning, China)

Abstract:

The linear combination of certain partition of unity, subordinate to certain open covering of a compact set, is proved to be capable of approximating to a continuous function at arbitrarily precision. By using proper open covering and partition of unity, the robust nonlinear controllers and adaptive laws are designed for a class of nonlinear systems with uncertainties. The states and parameters of the closed-loop systems can be stabilized in the meaning of UUB ( uniformly ultimately bounded) via the robust nonlinear controllers and adaptive laws. Finally, an example shows the validity of method in this paper.

Key words: Partition of unity Approximating theorem Uncertain system UUB