李代数秩条件的横向周期函数表征

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) Pub Date : 2000-12-12 DOI:10.1109/CDC.2000.912338

P. Morin, C. Samson

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引用次数: 85

摘要

李代数秩条件在非线性系统控制理论中占有重要地位。我们证明了一组光滑控制向量场满足这个条件等价于光滑横向周期函数的存在性。概述的证明——细节可以在Morin和Samson(2000)中找到——是建设性的，并为确定这些函数提供了一种方法。这是通过一个例子来说明的。

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A characterization of the Lie algebra rank condition by transverse periodic functions

The Lie algebra rank condition plays a central role in nonlinear systems control theory. We show that the satisfaction of this condition by a set of smooth control vector fields is equivalent to the existence of smooth transverse periodic functions. The proof outlined-details can be found in Morin and Samson (2000)-is constructive and provides a method for the determination of such functions. This is illustrated by an example.

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Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)

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